TY - JOUR

T1 - Complete classification of algebras of level two

AU - Kaygorodov, Ivan

AU - Volkov, Yury

PY - 2019/7/1

Y1 - 2019/7/1

N2 - The main result of the paper is the classification of all (nonassociative) algebras of level two, i.e., such algebras that maximal chains of nontrivial degenerations starting at them have length two. During this classification we obtain an estimation of the level of an algebra via its generation type, i.e., the maximal dimension of its one generated subalgebra. Also we describe all degenerations and levels of algebras of the generation type 1 with a square zero ideal of codimen-sion 1.

AB - The main result of the paper is the classification of all (nonassociative) algebras of level two, i.e., such algebras that maximal chains of nontrivial degenerations starting at them have length two. During this classification we obtain an estimation of the level of an algebra via its generation type, i.e., the maximal dimension of its one generated subalgebra. Also we describe all degenerations and levels of algebras of the generation type 1 with a square zero ideal of codimen-sion 1.

KW - Degeneration

KW - Level of algebra

KW - Orbit closure

UR - http://www.scopus.com/inward/record.url?scp=85068622654&partnerID=8YFLogxK

U2 - 10.17323/1609-4514-2019-19-3-485-521

DO - 10.17323/1609-4514-2019-19-3-485-521

M3 - Article

AN - SCOPUS:85068622654

VL - 19

SP - 485

EP - 521

JO - Moscow Mathematical Journal

JF - Moscow Mathematical Journal

SN - 1609-3321

IS - 3

ER -