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Bilinear complexity of algebras and the Chudnovsky-Chudnovsky interpolation method
Bilinear complexity of algebras Chudnovsky-Chudnovsky interpolation method Computational Complexity
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...
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 ...
An approach, based on Jucys–Murphy elements, to the representation theory of cy-clotomic Hecke algebras is developed. The maximality (in the cyclotomic Hecke algebra)of the set of the Jucys–Murphy ele...
On commutative, operator amenable subalgebras of finite von Neumann algebras
On commutative operator amenable subalgebras finite von Neumann algebras
2011/2/23
An open question, raised independently by several authors, asks if a closed amenable subalgebra of B(H) must be similar to an amenable C-algebra; the question remains open
even for singly-generated ...
Presentations and Tietze Transformations of C*-algebras
C*-algebra Unitization Adjoint Functor Free Construction
2011/1/18
In this work, I develop a new view of presentation theory for C*-algebras, both unital and non-unital, heavily grounded in classical notions from algebra. In particular, I introduce Tietze transformat...
Moyal multiplier algebras of the test function spaces of type S
Moyal multiplier algebras test function spaces of type S
2011/1/17
The Gel’fand-Shilov spaces of type S are considered as topological algebras with respect
to the Moyal star product and their corresponding algebras of multipliers are defined and
investigated.
Essential dimension of simple algebras in positive characteristic
Essential dimension simple algebras positive characteristic
2011/2/24
Let p be a prime integer, 1 ≤ s ≤ r integers, F a field of characteristic p.
Multiplicity-Free Representations of Divergence-Free Lie Algebras
divergence-free Lie algebra Cartan type graded modules irreducible modules
2011/2/21
Divergence-free Lie algebras (also known as the special Lie algebras of Cartan type) are
Lie algebras of volume-preserving transformation groups. They are simple in generic case.
Dokovic and Zhao fo...
On the Returning Arrows of Graded Self-injective Algebras
Arrows Graded Self-injective Algebras
2011/2/24
A translation quiver Q is a quiver with a mono quiver map ,called translation, defined on a subset of the vertices. Recently, varies construction gives rise to quiver obtained from the original one b...
Global and local Weyl modules for the untwisted multiloop Lie algebras were defined in [CFK] via homological properties. In this paper we extended the ideas to give a categorical definition of the Wey...
Topological algebras of rapidly decreasing matrices and generalizations
Rapidly decreasing matrix weighted matrix algebra continuous inverse algebra
2011/2/21
It is a folklore fact that the rapidly decreasing matrices of countable size form an associative topological algebra whose set of quasi-invertible elements is open, and such that the quasi-inversion m...
I give a simpler proof of the generalisation of Engel’s Theorem to Leibniz algebras.
We study algebras that are isotopic to Hurwitz algebras. Isomorphism classes of such algebras are shown to correspond to orbits of a certain group action. An explicit, geometrically
intutive descript...
In this paper, linear bases for the partially commutative Lie alge-bras are found. The method of the Gr¨obner–Shirshov bases is used.
Super duality and homology of unitarizable modules of Lie algebras
Super duality homology of unitarizable modules of Lie algebras
2011/1/18
The u-homology formulas for unitarizable modules at negative levels over classical Lie algebras of infinite rank of types gl(n), sp(2n) and so(2n) are obtained.As a consequence, we recover the Enright...