Download or read book A von Neumann Algebra Approach to Quantum Metrics Quantum Relations written by Greg Kuperberg and published by American Mathematical Soc.. This book was released on 2012 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: In A von Neumann Algebra Approach to Quantum Metrics, Kuperberg and Weaver propose a new definition of quantum metric spaces, or W*-metric spaces, in the setting of von Neumann algebras. Their definition effectively reduces to the classical notion in the atomic abelian case, has both concrete and intrinsic characterizations, and admits a wide variety of tractable examples. A natural application and motivation of their theory is a mutual generalization of the standard models of classical and quantum error correction. In Quantum Relations Weaver defines a ``quantum relation'' on a von Neumann algebra $\mathcal{M}\subseteq\mathcal{B}(H)$ to be a weak* closed operator bimodule over its commutant $\mathcal{M}'$. Although this definition is framed in terms of a particular representation of $\mathcal{M}$, it is effectively representation independent. Quantum relations on $l^\infty(X)$ exactly correspond to subsets of $X^2$, i.e., relations on $X$. There is also a good definition of a ``measurable relation'' on a measure space, to which quantum relations partially reduce in the general abelian case. By analogy with the classical setting, Weaver can identify structures such as quantum equivalence relations, quantum partial orders, and quantum graphs, and he can generalize Arveson's fundamental work on weak* closed operator algebras containing a masa to these cases. He is also able to intrinsically characterize the quantum relations on $\mathcal{M}$ in terms of families of projections in $\mathcal{M}{\overline{\otimes}} \mathcal{B}(l^2)$.
Download or read book A Von Neumann Algebra Approach to Quantum Metrics written by Greg Kuperberg and published by . This book was released on 2012 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: We define a "quantum relation" on a von Neumann algebra M⊆B(H) to be a weak* closed operator bimodule over its commutant M′. Although this definition is framed in terms of a particular representation of M, it is effectively representation independent. Quantum relations on l∞(X) exactly correspond to subsets of X2, i.e., relations on X. There is also a good definition of a "measurable relation" on a measure space, to which quantum relations partially reduce in the general abelian case. By analogy with the classical setting, we can identify structures such as quantum equivalence relations, quantum partial orders, and quantum graphs, and we can generalize Arveson's fundamental work on weak* closed operator algebras containing a masa to these cases. We are also able to intrinsically characterize the quantum relations on M in terms of families of projections in M⊗ ̄B(l2).
Download or read book A von Neumann Algebra Approach to Quantum Metrics Quantum Relations written by Greg Kuperberg and published by American Mathematical Soc.. This book was released on 2011 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Extended Graphical Calculus for Categorified Quantum sl 2 written by Mikhail Khovanov and published by American Mathematical Soc.. This book was released on 2012 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: In an earlier paper, Aaron D. Lauda constructed a categorification of the Beilinson-Lusztig-MacPherson form of the quantum sl(2); here he, Khovanov, Marco Mackaay, and Marko Stosic enhance the graphical calculus he introduced to include two-morphisms between divided powers one-morphisms and their compositions. They obtain explicit diagrammatical formulas for the decomposition of products of divided powers one-morphisms as direct sums of indecomposable one-morphisms, which are in a bijection with the Lusztig canonical basis elements. Their results show that one of Lauda's main results holds when the 2-category is defined over the ring of integers rather than over a field. The study is not indexed. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com).
Download or read book Hopf Algebras and Congruence Subgroups written by Yorck Sommerhäuser and published by American Mathematical Soc.. This book was released on 2012 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: We prove that the kernel of the action of the modular group on the center of a semisimple factorizable Hopf algebra is a congruence subgroup whenever this action is linear. If the action is only projective, we show that the projective kernel is a congruence subgroup. To do this, we introduce a class of generalized Frobenius-Schur indicators and endow it with an action of the modular group that is compatible with the original one.
Download or read book Finite Order Automorphisms and Real Forms of Affine Kac Moody Algebras in the Smooth and Algebraic Category written by Ernst Heintze and published by American Mathematical Soc.. This book was released on 2012 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt: Heintze and Gross discuss isomorphisms between smooth loop algebras and of smooth affine Kac-Moody algebras in particular, and automorphisms of the first and second kinds of finite order. Then they consider involutions of the first and second kind, and make the algebraic case. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com).
Download or read book The Reflective Lorentzian Lattices of Rank 3 written by Daniel Allcock and published by American Mathematical Soc.. This book was released on 2012-10-31 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: "November 2012, volume 220, Number 1033 (first of 4 numbers)."
Download or read book Character Identities in the Twisted Endoscopy of Real Reductive Groups written by Paul Mezo and published by American Mathematical Soc.. This book was released on 2013-02-26 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suppose $G$ is a real reductive algebraic group, $\theta$ is an automorphism of $G$, and $\omega$ is a quasicharacter of the group of real points $G(\mathbf{R})$. Under some additional assumptions, the theory of twisted endoscopy associates to this triple real reductive groups $H$. The Local Langlands Correspondence partitions the admissible representations of $H(\mathbf{R})$ and $G(\mathbf{R})$ into $L$-packets. The author proves twisted character identities between $L$-packets of $H(\mathbf{R})$ and $G(\mathbf{R})$ comprised of essential discrete series or limits of discrete series.
Download or read book Chevalley Supergroups written by Rita Fioresi and published by American Mathematical Soc.. This book was released on 2012 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the framework of algebraic supergeometry, the authors give a construction of the scheme-theoretic supergeometric analogue of split reductive algebraic group-schemes, namely affine algebraic supergroups associated to simple Lie superalgebras of classical type. In particular, all Lie superalgebras of both basic and strange types are considered. This provides a unified approach to most of the algebraic supergroups considered so far in the literature, and an effective method to construct new ones. The authors' method follows the pattern of a suitable scheme-theoretic revisitation of Chevalley's construction of semisimple algebraic groups, adapted to the reductive case. As an intermediate step, they prove an existence theorem for Chevalley bases of simple classical Lie superalgebras and a PBW-like theorem for their associated Kostant superalgebras.
Download or read book On L Packets for Inner Forms of SL n written by Kaoru Hiraga and published by American Mathematical Soc.. This book was released on 2012 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of $L$-indistinguishability for inner forms of $SL_2$ has been established in the well-known paper of Labesse and Langlands (L-indistinguishability forSL$(2)$. Canad. J. Math. 31 (1979), no. 4, 726-785). In this memoir, the authors study $L$-indistinguishability for inner forms of $SL_n$ for general $n$. Following the idea of Vogan in (The local Langlands conjecture. Representation theory of groups and algebras, 305-379, Contemp. Math. 145 (1993)), they modify the $S$-group and show that such an $S$-group fits well in the theory of endoscopy for inner forms of $SL_n$.
Download or read book Elliptic Integrable Systems written by Idrisse Khemar and published by American Mathematical Soc.. This book was released on 2012 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, the author studies all the elliptic integrable systems, in the sense of C, that is to say, the family of all the $m$-th elliptic integrable systems associated to a $k^\prime$-symmetric space $N=G/G_0$. The author describes the geometry behind this family of integrable systems for which we know how to construct (at least locally) all the solutions. The introduction gives an overview of all the main results, as well as some related subjects and works, and some additional motivations.
Download or read book Infinite Dimensional Representations of 2 Groups written by John C. Baez and published by American Mathematical Soc.. This book was released on 2012 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: Just as groups can have representations on vector spaces, 2-groups have representations on 2-vector spaces, but Lie 2-groups typically have few representations on the finite-dimensional 2-vector spaces introduced by Kapranov and Voevodsky. Therefore, Crane, Sheppeard, and Yetter introduced certain infinite-dimensional 2-vector spaces, called measurable categories, to study infinite-dimensional representations of certain Lie 2-groups, and German and North American mathematicians continue that work here. After introductory matters, they cover representations of 2-groups, and measurable categories, representations on measurable categories. There is no index. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com).
Download or read book Connes Chern Character for Manifolds with Boundary and Eta Cochains written by Matthias Lesch and published by American Mathematical Soc.. This book was released on 2012 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: "November 2012, volume 220, number (end of volume)."
Download or read book Modular Branching Rules for Projective Representations of Symmetric Groups and Lowering Operators for the Supergroup Q n written by Aleksandr Sergeevich Kleshchëv and published by American Mathematical Soc.. This book was released on 2012 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are two approaches to projective representation theory of symmetric and alternating groups, which are powerful enough to work for modular representations. One is based on Sergeev duality, which connects projective representation theory of the symmetric group and representation theory of the algebraic supergroup $Q(n)$ via appropriate Schur (super)algebras and Schur functors. The second approach follows the work of Grojnowski for classical affine and cyclotomic Hecke algebras and connects projective representation theory of symmetric groups in characteristic $p$ to the crystal graph of the basic module of the twisted affine Kac-Moody algebra of type $A_{p-1}^{(2)}$. The goal of this work is to connect the two approaches mentioned above and to obtain new branching results for projective representations of symmetric groups.
Download or read book Pseudo Differential Operators with Discontinuous Symbols Widom s Conjecture written by Aleksandr Vladimirovich Sobolev and published by American Mathematical Soc.. This book was released on 2013-02-26 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Relying on the known two-term quasiclassical asymptotic formula for the trace of the function $f(A)$ of a Wiener-Hopf type operator $A$ in dimension one, in 1982 H. Widom conjectured a multi-dimensional generalization of that formula for a pseudo-differential operator $A$ with a symbol $a(\mathbf{x}, \boldsymbol{\xi})$ having jump discontinuities in both variables. In 1990 he proved the conjecture for the special case when the jump in any of the two variables occurs on a hyperplane. The present paper provides a proof of Widom's Conjecture under the assumption that the symbol has jumps in both variables on arbitrary smooth bounded surfaces.
Download or read book A Study of Singularities on Rational Curves Via Syzygies written by David A. Cox and published by American Mathematical Soc.. This book was released on 2013-02-26 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: Consider a rational projective curve $\mathcal{C}$ of degree $d$ over an algebraically closed field $\pmb k$. There are $n$ homogeneous forms $g_{1},\dots, g_{n}$ of degree $d$ in $B=\pmb k[x, y]$ which parameterize $\mathcal{C}$ in a birational, base point free, manner. The authors study the singularities of $\mathcal{C}$ by studying a Hilbert-Burch matrix $\varphi$ for the row vector $[g_{1},\dots, g_{n}]$. In the ``General Lemma'' the authors use the generalized row ideals of $\varphi$ to identify the singular points on $\mathcal{C}$, their multiplicities, the number of branches at each singular point, and the multiplicity of each branch. Let $p$ be a singular point on the parameterized planar curve $\mathcal{C}$ which corresponds to a generalized zero of $\varphi$. In the `'triple Lemma'' the authors give a matrix $\varphi'$ whose maximal minors parameterize the closure, in $\mathbb{P}^{2}$, of the blow-up at $p$ of $\mathcal{C}$ in a neighborhood of $p$. The authors apply the General Lemma to $\varphi'$ in order to learn about the singularities of $\mathcal{C}$ in the first neighborhood of $p$. If $\mathcal{C}$ has even degree $d=2c$ and the multiplicity of $\mathcal{C}$ at $p$ is equal to $c$, then he applies the Triple Lemma again to learn about the singularities of $\mathcal{C}$ in the second neighborhood of $p$. Consider rational plane curves $\mathcal{C}$ of even degree $d=2c$. The authors classify curves according to the configuration of multiplicity $c$ singularities on or infinitely near $\mathcal{C}$. There are $7$ possible configurations of such singularities. They classify the Hilbert-Burch matrix which corresponds to each configuration. The study of multiplicity $c$ singularities on, or infinitely near, a fixed rational plane curve $\mathcal{C}$ of degree $2c$ is equivalent to the study of the scheme of generalized zeros of the fixed balanced Hilbert-Burch matrix $\varphi$ for a parameterization of $\mathcal{C}$.
Download or read book Vector Bundles on Degenerations of Elliptic Curves and Yang Baxter Equations written by Igor Burban and published by American Mathematical Soc.. This book was released on 2012 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: "November 2012, volume 220, number 1035 (third of 4 numbers)."
