Double Hom-Associative Algebra and Double Hom–Lie Bialgebra
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DOI: 10.1007/s00006-019-1028-2
Abstract: Recently, Hom-structures have been widely investigated in literature. In this paper, we introduce the conceptions of double Hom-associative algebras and double Hom–Lie bialgebras, and give a necessary and sufficient condition for double Hom-associative algebras to… read more here.
Keywords: hom; hom lie; hom associative; associative algebras ... See more keywords
Associative Algebras with a Distributive Lattice of Subalgebras
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DOI: 10.1007/s10469-020-09608-6
Abstract: We give a full description of associative algebras over an arbitrary field, whose subalgebra lattice is distributive. All such algebras are commutative, their nil-radical is at most two-dimensional, and the factor algebra with respect to… read more here.
Keywords: associative algebras; distributive lattice; algebras distributive; lattice subalgebras ... See more keywords
EA-Matrix Integrals of Associative Algebras and Equivariant Localization
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DOI: 10.1007/s40598-019-00111-0
Abstract: The EA-matrix integrals, introduced in Barannikov (Comptes Rendus Math 348:359–362, 2006), are studied in the case of graded associative algebras with odd or even scalar product. I prove that the EA-matrix integrals for associative algebras… read more here.
Keywords: matrix integrals; associative algebras; algebras equivariant; integrals associative ... See more keywords
Metabelian Associative Algebras
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DOI: 10.1007/s40840-015-0157-6
Abstract: Metabelian algebras are introduced and it is shown that an algebra A is metabelian if and only if A is a nilpotent algebra having the index of nilpotency at most 3, i.e. $$x y z… read more here.
Keywords: metabelian algebras; associative algebras; metabelian associative;
A class of continuous non-associative algebras arising from algebraic groups including $E_8$
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DOI: 10.1017/fms.2020.66
Abstract: Abstract We give a construction that takes a simple linear algebraic group G over a field and produces a commutative, unital, and simple non-associative algebra A over that field. Two attractions of this construction are… read more here.
Keywords: arising algebraic; non associative; class continuous; associative algebras ... See more keywords
Gröbner–Shirshov bases for pre-associative algebras
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DOI: 10.1080/00927872.2017.1304552
Abstract: ABSTRACT We develop Gröbner–Shirshov bases technique for pre-associative (dendriform) algebras and prove a version of composition-diamond lemma. read more here.
Keywords: bases pre; shirshov bases; pre associative; associative algebras ... See more keywords
Weakly associative algebras, Poisson algebras and deformation quantization
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DOI: 10.1080/00927872.2021.1909058
Abstract: Abstract Weakly associative algebras are a class of Lie-admissible algebras that generalize associative algebras and useful to extend the class of formal deformations of associative commutative algebras. Thus we obtain a new method of determining… read more here.
Keywords: algebras poisson; poisson algebras; quantization; associative algebras ... See more keywords
AXES IN NON-ASSOCIATIVE ALGEBRAS
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DOI: 10.3906/mat-2109-60
Abstract: “Fusion rules” are laws of multiplication among eigenspaces of an idempotent. This terminology is relatively new and is closely related to axial algebras, introduced recently by Hall, Rehren and Shpectorov. Axial algebras, in turn, are… read more here.
Keywords: associative algebras; axes non; non associative;
On a Lie Algebraic Approach to Abelian Extensions of Associative Algebras
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DOI: 10.4153/s0008439520000193
Abstract: Abstract By using a representation of a Lie algebra on the second Hochschild cohomology group, we construct an obstruction class to extensibility of derivations and a short exact sequence of Wells type for an abelian… read more here.
Keywords: extensions associative; approach abelian; abelian extensions; algebraic approach ... See more keywords