All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 14 Next

Displaying 261 – 280 of 534

Showing per page

Some remarks on the Akivis algebras and the Pre-Lie algebras

Yuqun Chen, Yu Li (2011)

Czechoslovak Mathematical Journal

In this paper, by using the Composition-Diamond lemma for non-associative algebras invented by A. I. Shirshov in 1962, we give Gröbner-Shirshov bases for free Pre-Lie algebras and the universal enveloping non-associative algebra of an Akivis algebra, respectively. As applications, we show I. P. Shestakov’s result that any Akivis algebra is linear and D. Segal’s result that the set of all good words in X * * forms a linear basis of the free Pre-Lie algebra PLie ( X ) generated by the set X . For completeness,...

Spectral sequences for commutative Lie algebras

Friedrich Wagemann (2020)

Communications in Mathematics

We construct some spectral sequences as tools for computing commutative cohomology of commutative Lie algebras in characteristic 2 . In a first part, we focus on a Hochschild-Serre-type spectral sequence, while in a second part we obtain spectral sequences which compare Chevalley-Eilenberg-, commutative- and Leibniz cohomology. These methods are illustrated by a few computations.

Square subgroups of rank two abelian groups

A. M. Aghdam, A. Najafizadeh (2009)

Colloquium Mathematicae

Let G be an abelian group and ◻ G its square subgroup as defined in the introduction. We show that the square subgroup of a non-homogeneous and indecomposable torsion-free group G of rank two is a pure subgroup of G and that G/◻ G is a nil group.

Structure theory for the group algebra of the symmetric group, with applications to polynomial identities for the octonions

Murray R. Bremner, Sara Madariaga, Luiz A. Peresi (2016)

Commentationes Mathematicae Universitatis Carolinae

This is a survey paper on applications of the representation theory of the symmetric group to the theory of polynomial identities for associative and nonassociative algebras. In §1, we present a detailed review (with complete proofs) of the classical structure theory of the group algebra 𝔽 S n of the symmetric group S n over a field 𝔽 of characteristic 0 (or p > n ). The goal is to obtain a constructive version of the isomorphism ψ : ⨁ λ M d λ ( 𝔽 ) ⟶ 𝔽 S n where λ is a partition of n and d λ counts the standard tableaux of shape λ ....

Subloops of sedenions

Benard M. Kivunge, Jonathan D. H Smith (2004)

Commentationes Mathematicae Universitatis Carolinae

This note investigates sedenion multiplication from the standpoint of loop theory. New two-sided loops are obtained within the version of the sedenions introduced by the second author. Conditions are given for the satisfaction of standard loop-theoretical identities within these loops.

Sur la catégorie de Lusternik-Schnirelmann des algèbres de cochaînes

Bitjong Ndombol (1991)

Annales de l'institut Fourier

Nous introduisons une nouvelle définition d’un invariant bi M cat pour une algèbre de cochaînes A connexe et 1-connexe, de type fini sur un corps k de caractéristique quelconque, et nous montrons d’une part, qu’il coïncide avec l’invariant 𝒜 cat introduit par S. Halperin et J.-M. Lemaire et d’autre part, qu’il est invariant par extension de corps et qu’il vérifie la conjecture de Ganéa.

Sur une algèbre Q-symétrique

A. Guichardet (1997)

Annales Polonici Mathematici

We establish several properties of a quadratic algebra over a field k, which is a deformation of the symmetric algebra Sk³. In particular, we prove that A is an integral domain, noetherian and Koszul; we compute its first Hochschild cohomology group; we determine the corresponding Poisson structure on k³ and its symplectic leaves; we define an involution on A and describe the corresponding irreducible involutive representations.

Currently displaying 261 – 280 of 534