Capelli identities for Lie superalgebras
Caractères semi-simples de , corps local non archimédien
Soit un corps local non archimédien de caractéristique résiduelle différente de et . Nous définissons strates semi-simples et caractères semi-simples pour le groupe exceptionnel à l’aide des objets analogues pour le groupe , des automorphismes de trialité et d’une correspondance de Glauberman. Nous construisons alors les types semi-simples associés et nous donnons des conditions suffisantes pour que ces types s’induisent irréductiblement, obtenant ainsi des représentations supercuspidales...
Cartan subalgebras, weight spaces, and criterion of solvability of finite dimensional Leibniz algebras.
In this work the properties of Cartan subalgebras and weight spaces of finite dimensional Lie algebras are extended to the case of Leibniz algebras. Namely, the relation between Cartan subalgebras and regular elements are described, also an analogue of Cartan s criterion of solvability is proved.
Cayley-Dickson Construction
Cayley-Dickson construction produces a sequence of normed algebras over real numbers. Its consequent applications result in complex numbers, quaternions, octonions, etc. In this paper we formalize the construction and prove its basic properties.
Central closure of prime non commutative Jordan algebras with nonzero socle
Central series for groups with action and Leibniz algebras.
Certain partitions on a set and their applications to different classes of graded algebras
Let and be two pointed sets. Given a family of three maps , this family provides an adequate decomposition of as the orthogonal disjoint union of well-described -invariant subsets. This decomposition is applied to the structure theory of graded involutive algebras, graded quadratic algebras and graded weak -algebras.
Certain simple maximal subfields in division rings
Let be a division ring finite dimensional over its center . The goal of this paper is to prove that for any positive integer there exists the th multiplicative derived subgroup such that is a maximal subfield of . We also show that a single depth- iterated additive commutator would generate a maximal subfield of
Certaines algèbres non associatives simples définies par la transvection des formes binaires.
Characters of irreducible representations of simple Lie superalgebras.
Charakterisierung symmetrischer R-Räume durch ihre Einheitsgitter.
Classification of 4-dimensional nilpotent complex Leibniz algebras.
Classification of all associative mono--ary algebras with 2 elements.
Classification of p-adic 6-dimensional filiform Leibniz algebras by solutions of x q = a
We study the p-adic equation x q = a over the field of p-adic numbers. We construct an algorithm which gives a solvability criteria in the case of q = p m and present a computer program to compute the criteria for any fixed value of m ≤ p − 1. Moreover, using this solvability criteria for q = 2; 3; 4; 5; 6, we classify p-adic 6-dimensional filiform Leibniz algebras.
Classification of the Steiner quadruple systems of cardinality 32
Classifying two-dimensional hyporeductive triple algebra.
Coherent unit actions on regular operads and Hopf algebras.
Cohomology of deformation parameters of diagonal noncommutative nonassociative graded algebras.
Cohomology of Hom-Lie superalgebras and -deformed Witt superalgebra
Hom-Lie algebra (superalgebra) structure appeared naturally in -deformations, based on -derivations of Witt and Virasoro algebras (superalgebras). They are a twisted version of Lie algebras (superalgebras), obtained by deforming the Jacobi identity by a homomorphism. In this paper, we discuss the concept of -derivation, a representation theory, and provide a cohomology complex of Hom-Lie superalgebras. Moreover, we study central extensions. As application, we compute derivations and the second...
Cohomology ring of n-Lie algebras.
Natural graded Lie brackets on the space of cochains of n-Leibniz and n-Lie algebras are introduced. It turns out that these brackets agree under the natural embedding introduced by Gautheron. Moreover, n-Leibniz and n-Lie algebras turn to be canonical structures for these brackets in a similar way in which associative algebras (respectively, Lie algebras) are canonical structures for the Gerstenhaber bracket (respectively, Nijenhuis-Richardson bracket).