SPLIT REGULAR HOM-LEIBNIZ COLOR 3-ALGEBRAS

Author(s)

Kaygorodov, Ivan ^[1] ; Popov, Yury ^[2]

Affiliation

^[1] Univ Fed ABC, CMCC, Av Estado, 5001 Bangu, BR-09210580 Santo Andre, SP - Brazil

^[2] Univ Estadual Campinas, IMECC, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: Colloquium Mathematicum; v. 157, n. 2, p. 251-277, 2019.
• Web of Science Citations: 0

Abstract

We introduce and describe the class of split regular Hom-Leibniz color 3-algebras as the natural extension of the class of split Lie algebras and superalgebras. More precisely, we show that any such split regular Hom-Leibniz color 3-algebra T is of the form T = U + Sigma(j) I-j with U a subspace of the 0-root space T-0, and I-j an ideal of T such that for j not equal k, {[}T, I-j, I-k] + {[}I-j, T, I-k] + {[}I-j, I-k, T] = 0.( )( )( ) Moreover, if T is of maximal length, we characterize the simplicity of T in terms of a connectivity property in its set of non-zero roots. (AU)

• FAPESP's process: 16/16445-0 - Representations of (super)algebras of Jordan type
• Grantee: Yury Popov
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 17/15437-6 - N-ary split strutures
• Grantee: Ivan Kaygorodov
• Support Opportunities: Scholarships abroad - Research