Conservative algebras of 2-dimensional algebras

Author(s)

Kaygorodov, Ivan ^{[1, 2]} ; Lopatin, Artem ^{[3, 4]} ; Popov, Yury ^{[5, 1]}

Affiliation

^[1] Sobolev Inst Math, Novosibirsk 630090 - Russia

^[2] Univ Fed ABC, CMCC, Santo Andre - Brazil

^[3] Univ Estadual Campinas, IMECC, BR-13083859 Campinas, SP - Brazil

^[4] Sobolev Inst Math, Omsk Branch, Omsk 664099 - Russia

^[5] Novosibirsk State Univ, Novosibirsk 630090 - Russia

• Document type: Journal article
• Source: Linear Algebra and its Applications; v. 486, p. 255-274, DEC 1 2015.
• Web of Science Citations: 3

Abstract

In 1990 Kantor introduced the conservative algebra W(n) of all algebras (i.e. bilinear maps) on the n-dimensional vector space. In case n > 1 the algebra W(n) does not belong to well-known classes of algebras (such as associative, Lie, Jordan, Leibniz algebras). We describe the algebra of all derivations of W(2) and subalgebras of W(2) of codimension one. We also study similar problems for the algebra W-2 of all commutative algebras on the two-dimensional vector space and the algebra S-2 of all commutative algebras with trace zero multiplication on the two-dimensional space. (C) 2015 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 11/51132-9 - General Poisson algebras and generalized derivarions
• Grantee: Ivan Kaygorodov
• Support Opportunities: Scholarships in Brazil - Post-Doctoral