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New Irreducible Modules for Heisenberg and Affine Lie Algebras
Irreducible Modules Heisenberg Affine Lie Algebras
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2011/8/25
Abstract: We study $\mathbb Z$-graded modules of nonzero level with arbitrary weight multiplicities over Heisenberg Lie algebras and the associated generalized loop modules over affine Kac-Moody Lie a...
Filtered Lie conformal algebras whose associated graded algebras are isomorphic to that of general conformal algebra $gc_1$
Lie conformal algebras filtered algebras general conformal algebras second cohomology groups
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2011/8/25
Abstract: Let $G$ be a filtered Lie conformal algebra whose associated graded conformal algebra is isomorphic to that of general conformal algebra $gc_1$. In this paper, we prove that $G\cong gc_1$ or...
Twisted Frobenius-Schur indicators for Hopf algebras
semisimple Hopf algebra character Frobenius–Schur indicator automorphism
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2011/8/25
Abstract: The classical Frobenius-Schur indicators for finite groups are character sums defined for any representation and any integer m greater or equal to 2. In the familiar case m=2, the Frobenius-...
A remarkable contraction of semisimple Lie algebras
Inonu-Wigner contraction coadjoint representation algebra of invariants orbit
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2011/8/25
Abstract: Recently, E.Feigin introduced a very interesting contraction $\mathfrak q$ of a semisimple Lie algebra $\mathfrak g$ (see arXiv:1007.0646 and arXiv:1101.1898). We prove that these non-reduct...
Universal equivalence of partially commutative metabelian Lie algebras
Lie algebras Universal equivalence Rings and Algebras
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2011/8/23
Abstract: In this paper, we find a criterium for universal equivalence of partially commutative Lie algebras whose defining graphs are trees. Besides, we obtain bases for partially commutative metabel...
Representations of Rational Cherednik Algebras in Positive Characteristic
Rational Cherednik Algebras Positive Characteristic Representation Theory
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2011/8/24
Abstract: We study rational Cherednik algebras over an algebraically closed field of positive characteristic. We first prove several general results about category O, and then focus on rational Chered...
Stratifications of derived categories from tilting modules over tame hereditary algebras
Adele ring Recollement Stratification Tame hereditary algebra Tilting module Universal localization
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2011/8/24
Abstract: n this paper, we consider the endomorphism algebras of infinitely generated tilting modules of the form $R_{\mathcal U}\oplus R_{\mathcal U}/R$ over tame hereditary $k$-algebras $R$ with $k$...
C*-algebras with the weak expectation property and a multivariable analogue of Ando's theorem on the numerical radius
C*-algebras the weak expectation property Ando's theorem the numerical radius
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2011/8/23
Abstract: A classic theorem of T. Ando characterises operators that have numerical radius at most one as operators that admit a certain positive 2x2 operator matrix completion. In this paper we consid...
Koszul duality of affine Kac-Moody algebras and cyclotomic rational DAHA
Koszul duality affine Kac-Moody algebras cyclotomic rational DAHA
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2011/8/22
Abstract: We give a proof of the parabolic/singular Koszul duality for the category O of affine Kac-Moody algebras. The main new tool is a relation between moment graphs and finite codimensional affin...
Bilinear complexity of algebras and the Chudnovsky-Chudnovsky interpolation method
Bilinear complexity of algebras Chudnovsky-Chudnovsky interpolation method Computational Complexity
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2011/9/29
Abstract: We give new improvements to the Chudnovsky-Chudnovsky method that provides upper bounds on the bilinear complexity of multiplication in extensions of finite fields through interpolation on a...
Graphs and the (co)homology of Lie algebras
Graphs (co)homology Lie algebras
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2011/8/23
Abstract: In this paper, we develop a diamond graph theory and apply the theory to the (co)homology of the Lie algebra generated by positive systems of the classical semi-simple Lie algebras over the ...
Division Algebras, Supersymmetry and Higher Gauge Theory
Division Algebras Supersymmetry Higher Gauge Theory
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2011/7/26
Division Algebras, Supersymmetry and Higher Gauge Theory.
Clifford Algebras and Spinors
Clifford Algebras Spinors History and Overview
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2011/7/26
Abstract: Expository notes on Clifford algebras and spinors with a detailed discussion of Majorana, Weyl, and Dirac spinors. The paper is meant as a review of background material, needed, in particula...
Clifford Algebras and Spinors
Clifford Algebras Spinors
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2011/9/14
Expository notes on Clifford algebras and spinors with a detailed discussion of Majorana, Weyl, and Dirac spinors. The paper is meant as a review of background material, needed, in particular, in now ...
Surfaces immersed in Lie algebras associated with elliptic integrals
Generalized symmetries integrable models surfaces immersed in Lie algebras
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2011/7/26
Surfaces immersed in Lie algebras associated with elliptic integrals.