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Given an element P(X1, . . . ,Xd) of the free Lie K-algebra Ld, for any Lie algebra g we can consider the induced polynomial map P : gd → g. Assuming that K is an arbitrary field of characteristic 6= ...
We discuss an algebraic approach to propositional logic with side effects. To this end, we use Hoare’s conditional [1985], which is a ternary connective comparable to if-then-else. Starting from McCar...
Hyperbolic subalgebras of hyperbolic Kac-Moody algebras
Hyperbolic subalgebras hyperbolic Kac-Moody algebras
2011/1/18
We investigate regular hyperbolic subalgebras of hy-perbolic Kac-Moody algebras via their Weyl groups. We classify all subgroups relations between Weyl groups of hyperbolic Kac-Moody algebras, and sho...
Random partitions and asymptotic theory of symmetric groups, Hecke algebras and finite Chevalley groups
Random partitions asymptotic theory of symmetric groups Hecke algebras finite Chevalley groups
2011/2/22
Kit meanwhile had begun to frequent the Applied Mechanics Institute. Since Prandtl’s recent discovery of the boundary layer, things over there had been hopping, with intense inquiry into matters of li...
Stabilizers of Subspaces under Similitudes of the Klein Quadric, and Automorphisms of Heisenberg Algebras
Klein quadric Grassmann space automorphism orbit nilpotent Lie algebra Heisenberg algebra
2011/1/17
We determine the groups of automorphisms and their orbits for nilpotent Lie algebras of
class 2 and small dimension, over arbitrary fields (including the characteristic 2 case).
On the spectral theory of Rickart Ordered *-algebras
spectral theory Rickart Ordered *-algebras
2011/2/25
RO-algebras are defined and studied. For RO-algebra T , using properties of partial order, it is established that the set of bounded elements can be endowed with C-norm. The structure of commutativ...
Poisson algebras and symmetries of block-upper-triangular matrices
Poisson algebras symmetries of block-upper-triangular matrices
2011/2/25
Using the structure of algebroid of block-upper-triangular matri-ces composed from blocks of size m×m we obtain the Poisson brackets on the entries of these matrices and construct the braid-group acti...
On the description of the Leibniz algebras with nilindex n-3
description of the Leibniz algebras nilindex n-3
2011/1/20
In this paper we present the classification of a subclass of natu-rally graded Leibniz algebras. These n-dimensional Leibniz algebras have the characteristic sequence equal to (n−3, 3). For this...
A twisted generalization of Lie-Yamaguti algebras
Lie-Yamaguti algebra (i.e. generalized Lie triple system
2011/1/17
A twisted generalization of Lie-Yamaguti algebras, called Hom-Lie-Yamaguti algebras, is defined. Hom-Lie-Yamaguti algebras generalize Hom-Lie triple systems (and subsequently ternary Hom-Nambu algebra...
Homogeneous spaces, multi-moment maps and (2,3)-trivial algebras
Homogeneous spaces multi-moment maps (2,3)-trivial algebras
2011/1/17
For geometries with a closed three-form we briefly overview the notion of multimoment maps. We then give concrete examples of multi-moment maps for homogeneous hypercomplex and nearly K¨ahler manifold...
Based on invariant algebras, we introduce representations6−th of Lie algebras and representationsh4−thi of Leibniz algebras, give the extended P-B-W Theorems in the context of the new repr...
The purpose of this chapter is to give an introduction to the theory of cluster categories and cluster-tilted algebras, with some background on the theory of cluster algebras, which motivated these to...
Nonassociative strict deformation quantization of C*-algebras and nonassociative torus bundles
Nonassociative strict deformation quantization nonassociative torus bundles T-duality
2011/1/20
In this paper, we initiate the study of nonassociative strict deformation quantization of C-algebras with a torus action. We shall also present a definition of nonassociative principal
torus bundles...
Freeness of Linear and Quadratic Forms in von Neumann Algebras
Free random variables free convolutions a characterization of the semicircle law
2011/2/28
We characterize the semicircular distribution by freeness of linear and qua-dratic forms in noncommutative random variables from tracial W-probability spaces with relaxed moment conditions.
Duality for cochain DG algebras
Balanced dualizing complex Castelnuovo-Mumford re-gularity
2011/2/22
This paper develops a duality theory for connected cochain DG algebras, with particular emphasis on the non-com-mutative aspects.