Displaying similar documents to “On the degenerations of finite dimensional nilpotent complex Leibniz algebras.”

Pre-derivations and description of non-strongly nilpotent filiform Leibniz algebras

K.K. Abdurasulov, A.Kh. Khudoyberdiyev, M. Ladra, A.M. Sattarov (2021)

Communications in Mathematics

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In this paper we give the description of some non-strongly nilpotent Leibniz algebras. We pay our attention to the subclass of nilpotent Leibniz algebras, which is called filiform. Note that the set of filiform Leibniz algebras of fixed dimension can be decomposed into three disjoint families. We describe the pre-derivations of filiform Leibniz algebras for the first and second families and determine those algebras in the first two classes of filiform Leibniz algebras that are non-strongly...

On enveloping semigroups of nilpotent group actions generated by unipotent affine transformations of the torus

Rafał Pikuła (2010)

Studia Mathematica

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Let G be a group generated by a set of affine unipotent transformations T: X → X of the form T(x) = A x + α, where A is a lower triangular unipotent matrix, α is a constant vector, and X is a finite-dimensional torus. We show that the enveloping semigroup E(X,G) of the dynamical system (X,G) is a nilpotent group and find upper and lower bounds on its nilpotency class. Also, we obtain a description of E(X,G) as a quotient space.

Group Gradings on Free Algebras of Nilpotent Varieties of Algebras

Bahturin, Yuri (2012)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: Primary 16W50, 17B70; Secondary 16R10. The main result is the classification, up to isomorphism, of all gradings by arbitrary abelian groups on the finitely generated algebras that are free in a nilpotent variety of algebras over an algebraically closed field of characteristic zero. The research was supported by an NSERC Discovery Grant #227060-09

Affine Birman-Wenzl-Murakami algebras and tangles in the solid torus

Frederick M. Goodman, Holly Hauschild (2006)

Fundamenta Mathematicae

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The affine Birman-Wenzl-Murakami algebras can be defined algebraically, via generators and relations, or geometrically as algebras of tangles in the solid torus, modulo Kauffman skein relations. We prove that the two versions are isomorphic, and we show that these algebras are free over any ground ring, with a basis similar to a well known basis of the affine Hecke algebra.

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

Dietrich Burde (2006)

Open Mathematics

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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...

Unified computational approach to nilpotent algebra classification problems

Shirali Kadyrov, Farukh Mashurov (2021)

Communications in Mathematics

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In this article, we provide an algorithm with Wolfram Mathematica code that gives a unified computational power in classification of finite dimensional nilpotent algebras using Skjelbred-Sund method. To illustrate the code, we obtain new finite dimensional Moufang algebras.