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Cuntz-Pimsner algebras for subproduct systems
Cuntz-Pimsner algebras subproduct systems Operator Algebras
2011/9/6
Abstract: In this paper we generalize the notion of Cuntz-Pimsner algebras of $C^*$-correspondences to the setting of subproduct systems. The construction is justified in several ways, including the M...
Poisson Ideals in Cluster Algebras and the Spectra of Quantized Coordinate Rings
Poisson Ideals Cluster Algebras the Spectra of Quantized Coordinate Rings Quantum Algebra
2011/9/6
Abstract: We describe the Poisson ideals and attached symplectic geometry of a cluster algebra with compatible Poisson structure. We apply these results to determine the spectrum of a quantum cluster ...
Representation theory of three-dimensional Sklyanin algebras
noncommutative algebraic geometry representation theory supersymmetric string theory three-dimensional Sklyanin algebra
2011/9/9
Abstract: We determine the dimensions of irreducible representations of the three-dimensional Sklyanin algebras. This contributes to the study of marginal deformations of the N=4 super Yang-Mills theo...
Induced Cylindric Algebras of Choice Structures
epsilon calculus canonical model monadic algebra sigma complete Boolean algebra
2011/9/5
Abstract: One of the benefit properties implied by the extensionality axiom of Hilbert's epsilon calculus is that the calculus becomes complete with respect to the choice structures as semantics. Anot...
Deformation of algebras associated to group cocycles
deformation Fell bundle K-theory Operator Algebras
2011/9/5
Abstract: We define a deformation of algebras endowed with coaction of the reduced group algebras. The deformation parameter is given by a 2-cocycle over the group. We prove K-theory isomorphisms for ...
Deformation Expression for Elements of Algebras (III) --Generic product formula for *-exponentials of quadratic forms--
Weyl algebra Heisenberg Lie algebra meta-plectic groups spinor polar elements
2011/9/5
Abstract: In a noncommutative algebra there is no canonical way to express elements in univalent way, which is often called "ordering problem". In this note we give product formula of the Weyl algebra...
Enhanced Gauge Groups in N=4 Topological Amplitudes and Lorentzian Borcherds Algebras
Gauge Groups Topological Amplitudes Lorentzian Borcherds Algebras
2011/9/30
Abstract: We continue our study of algebraic properties of N=4 topological amplitudes in heterotic string theory compactified on T^2, initiated in arXiv:1102.1821. In this work we evaluate a particula...
Free group algebras in Malcev-Neumann skew fields of fractions
Division rings Malcev-Neumann series Rings and Algebras
2011/9/5
Abstract: Let K be a skew field and (G,<) an ordered group. We show that the skew field generated by the group ring K[G] inside the Malcev-Neumann series ring K((G;<)) contains noncommutative free gro...
Assembly maps with coefficients in topological algebras and the integral K-theoretic Novikov conjecture
topological algebras the integral K-theoretic Novikov conjecture K-Theory and Homology Algebraic Topology
2011/9/2
Abstract: We prove that any countable discrete and torsion free subgroup of a general linear group over an arbitrary field or a similar subgroup of an almost connected Lie group satisfies the integral...
Completely bounded representations of convolution algebras of locally compact quantum groups
Locally compact quantum group Fourier algebra completely bounded homomorphism corepresentation amenability
2011/9/1
Abstract: Given a locally compact quantum group $\G$, we study the question of when completely bounded homomorphisms $\pi:L^1(\mathbb G)\rightarrow\mathcal B(H)$ are similar to *-homomorphisms. By ana...
Classification of Simple Lie Algebras on a Lattice
Simple Lie Algebras Lattice Representation Theory Mathematical Physics
2011/9/1
Abstract: Let $\Lambda$ be a lattice of rank $n$. A Lie algebra on the lattice $\Lambda$ is a Lie algebra ${\cal L}=\oplus_{\lambda\in\Lambda}\,{\cal L}_{\lambda}$ such that $\dim\,{\cal L}_\lambda=1$...
C*-algebras nearly contained in type I algebras
C*-algebras Near inclusions Perturbations Type I C*-algebras Similarity Problem
2011/9/1
Abstract: In this paper we consider near inclusions $A\subseteq_\gamma B$ of C$^*$-algebras. We show that if $B$ is a separable type I C*-algebra and $A$ satisfies Kadison's similarity problem, then $...
Characterizations of all-derivable points in nest algebras
All-derivable point nest algebra derivable linear mapping at G
2011/9/1
Abstract: Let $\mathcal{A}$ be an operator algebra on a Hilbert space. We say that an element $G\in {\mathcal{A}}$ is an all-derivable point of ${\mathcal{A}}$ if every derivable linear mapping $\phi$...
On the representation dimension of artin algebras
dimension of artin algebras Representation Theory
2011/8/31
Abstract: The representation dimension of an artin algebra as introduced by M.Auslander in his Queen Mary Notes is the minimal possible global dimension of the endomorphism ring of a generator-cogener...
Abstract: Using the method of commutative algebra, we show that the set $\mathfrak{R}$ of nilpotent elements of a vertex algebra $V$ forms an ideal, and $V/\mathfrak{R}$ has no nonzero nilpotent eleme...