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 8 Next

Displaying 141 – 160 of 534

Showing per page

Left-symmetric algebras, or pre-Lie algebras in geometry and physics

Dietrich Burde (2006)

Open Mathematics

In this survey article we discuss the origin, theory and applications of left-symmetric algebras (LSAs in short) in geometry in physics. Recently Connes, Kreimer and Kontsevich have introduced LSAs in mathematical physics (QFT and renormalization theory), where the name pre-Lie algebras is used quite often. Already Cayley wrote about such algebras more than hundred years ago. Indeed, LSAs arise in many different areas of mathematics and physics. We attempt to give a survey of the fields where LSAs...

Leibniz A -algebras

David A. Towers (2020)

Communications in Mathematics

A finite-dimensional Lie algebra is called an A -algebra if all of its nilpotent subalgebras are abelian. These arise in the study of constant Yang-Mills potentials and have also been particularly important in relation to the problem of describing residually finite varieties. They have been studied by several authors, including Bakhturin, Dallmer, Drensky, Sheina, Premet, Semenov, Towers and Varea. In this paper we establish generalisations of many of these results to Leibniz algebras.

Leibniz cohomology for differentiable manifolds

Jerry M. Lodder (1998)

Annales de l'institut Fourier

We propose a definition of Leibniz cohomology, H L * , for differentiable manifolds. Then H L * becomes a non-commutative version of Gelfand-Fuks cohomology. The calculations of H L * ( R n ; R ) reduce to those of formal vector fields, and can be identified with certain invariants of foliations.

Lie commutators in a free diassociative algebra

A.S. Dzhumadil'daev, N.A. Ismailov, A.T. Orazgaliyev (2020)

Communications in Mathematics

We give a criterion for Leibniz elements in a free diassociative algebra. In the diassociative case one can consider two versions of Lie commutators. We give criterions for elements of diassociative algebras to be Lie under these commutators. One of them corresponds to Leibniz elements. It generalizes the Dynkin-Specht-Wever criterion for Lie elements in a free associative algebra.

Lie perfect, Lie central extension and generalization of nilpotency in multiplicative Lie algebras

Dev Karan Singh, Mani Shankar Pandey, Shiv Datt Kumar (2024)

Czechoslovak Mathematical Journal

This paper aims to introduce and explore the concept of Lie perfect multiplicative Lie algebras, with a particular focus on their connections to the central extension theory of multiplicative Lie algebras. The primary objective is to establish and provide proof for a range of results derived from Lie perfect multiplicative Lie algebras. Furthermore, the study extends the notion of Lie nilpotency by introducing and examining the concept of local nilpotency within multiplicative Lie algebras. The...

Localization in semicommutative (m,n)-rings

Lăcrimioara Iancu, Maria S. Pop (2000)

Discussiones Mathematicae - General Algebra and Applications

We give a construction for (m,n)-rings of quotients of a semicommutative (m,n)-ring, which generalizes the ones given by Crombez and Timm and by Paunić for the commutative case. We also study various constructions involving reduced rings and rings of quotients and give some functorial interpretations.

Morphisms in the category of finite-dimensional absolute valued algebras

Seidon Alsaody (2011)

Colloquium Mathematicae

This is a study of morphisms in the category of finite-dimensional absolute valued algebras whose codomains have dimension four. We begin by citing and transferring a classification of an equivalent category. Thereafter, we give a complete description of morphisms from one-dimensional algebras, partly via solutions of real polynomials, and a complete, explicit description of morphisms from two-dimensional algebras. We then give an account of the reducibility of the morphisms, and for the morphisms...

Currently displaying 141 – 160 of 534