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Conservative algebras of $2$-dimensional algebras, V | | Ivan Kaygorodov
; Dolores Martín Barquero
; Cándido Martín González
; | | Date: |
1 Jan 2023 | | Abstract: | The notion of conservative algebras appeared in a paper by Kantor in 1972.
Later, he defined the conservative algebra $W(n)$ of all algebras (i.e.
bilinear maps) on the $n$-dimensional vector space. If $n>1$, then the algebra
$W(n)$ does not belong to any well-known class of algebras (such as
associative, Lie, Jordan, or Leibniz algebras). It looks like $W(n)$ in the
theory of conservative algebras plays a similar role to the role of
$mathfrak{gl}_n$ in the theory of Lie algebras. Namely, an arbitrary
conservative algebra can be obtained from a universal algebra $W(n)$ for some
$n in mathbb{N}.$ The present paper is a part of a series of papers, which
dedicated to the study of the algebra $W(2)$ and its principal subalgebras. | | Source: | arXiv, 2301.00388 | | Services: | Forum | Review | PDF | Favorites | |
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