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Moscow Mathematical Journal

Volume 19, Issue 3, July–September 2019  pp. 485–521.

Complete Classification of Algebras of Level Two

Authors:  Ivan Kaygorodov (1) and Yury Volkov (2)
Author institution:(1) Universidade Federal do ABC, CMCC, Av. dos Estados, 5001 – Bangú, Santo André – SP, 09210-580, Brazil
(2) Sankt Peterburg state university, Vassilyevskiy ostrov, 14 liniya, 29V, Sankt-Peterburg 199178, Russia


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 codimension 1.

2010 Math. Subj. Class. 14D06, 14L30.

Keywords: Level of algebra, orbit closure, degeneration.

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