TY - JOUR
T1 - The algebraic and geometric classification of nilpotent terminal algebras
AU - Kaygorodov, Ivan
AU - Khrypchenko, Mykola
AU - Popov, Yury
N1 - Funding Information:
The first part of this work is supported by FAPESP 16/16445-0 , 18/15712-0 , 18/09299-2 ; CNPq 451499/2018-2 , 404649/2018-1 ; the President's “Program Support of Young Russian Scientists” (grant MK-2262.2019.1 ); by CMUP ( UID/MAT/00144/2019 ), which is funded by FCT with national (MCTES) and European structural funds through the programs FEDER , under the partnership agreement PT2020 ; by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through the project PTDC/MAT-PUR/31174/2017 . The second part of this work is supported by the Russian Science Foundation under grant 19-71-10016 . The authors thank Abror Khudoyberdiyev for constructive comments.
Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2021/6
Y1 - 2021/6
N2 - We give algebraic and geometric classifications of 4-dimensional complex nilpotent terminal algebras. Specifically, we find that, up to isomorphism, there are 41 one-parameter families of 4-dimensional nilpotent terminal (non-Leibniz) algebras, 18 two-parameter families of 4-dimensional nilpotent terminal (non-Leibniz) algebras, 2 three-parameter families of 4-dimensional nilpotent terminal (non-Leibniz) algebras, complemented by 21 additional isomorphism classes (see Theorem 13). The corresponding geometric variety has dimension 17 and decomposes into 3 irreducible components determined by the Zariski closures of a one-parameter family of algebras, a two-parameter family of algebras and a three-parameter family of algebras (see Theorem 15). In particular, there are no rigid 4-dimensional complex nilpotent terminal algebras.
AB - We give algebraic and geometric classifications of 4-dimensional complex nilpotent terminal algebras. Specifically, we find that, up to isomorphism, there are 41 one-parameter families of 4-dimensional nilpotent terminal (non-Leibniz) algebras, 18 two-parameter families of 4-dimensional nilpotent terminal (non-Leibniz) algebras, 2 three-parameter families of 4-dimensional nilpotent terminal (non-Leibniz) algebras, complemented by 21 additional isomorphism classes (see Theorem 13). The corresponding geometric variety has dimension 17 and decomposes into 3 irreducible components determined by the Zariski closures of a one-parameter family of algebras, a two-parameter family of algebras and a three-parameter family of algebras (see Theorem 15). In particular, there are no rigid 4-dimensional complex nilpotent terminal algebras.
KW - Algebraic classification
KW - Geometric classification
KW - Leibniz algebra
KW - Nilpotent algebra
KW - Terminal algebra
UR - http://www.scopus.com/inward/record.url?scp=85096220356&partnerID=8YFLogxK
U2 - 10.1016/j.jpaa.2020.106625
DO - 10.1016/j.jpaa.2020.106625
M3 - Article
AN - SCOPUS:85096220356
VL - 225
JO - Journal Of Pure And Applied Algebra
JF - Journal Of Pure And Applied Algebra
SN - 0022-4049
IS - 6
M1 - 106625
ER -