Degenerations of 3-dimensional nilpotent associative algebras over an algebraically closed field

2023/12/15 by Ivanova, N. M., Pallikaros, C. A.
#14D06 #14R20 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2312.09771

Abstract

We determine the complete degeneration picture inside the variety of nilpotent associative algebras of dimension 3 over an algebraically closed field of characteristic not equal to 2. Comparing with the discussion in [Ivanova N.M. and Pallikaros C.A., Degenerations of complex associative algebras of dimension three via Lie and Jordan algebras, \it Advances in Group Theory and Applications, 18 (2024), 41-79], for some of the arguments in the present article we needed to develop alternative techniques which are now valid over an arbitrary algebraically closed field. There is a dichotomy of cases concerning the results obtained, corresponding to whether the characteristic of the field is 2 or not.

Related

• Degenerations of complex associative algebras of dimension three via Lie and Jordan algebras
• On three-dimensional associative algebras
• Classification of nilpotent associative algebras of small dimension
• On degenerations of algebras over an arbitrary field
• Some classes of nilpotent associative algebras