Nilpotent evolution algebras over arbitrary fields

Abstract

The paper is devoted to the study of annihilator extensions of evolution algebras and suggests an approach to classify finite-dimensional nilpotent evolution algebras. Subsequently nilpotent evolution algebras of dimension up to four are classfied.

arXiv admin note: text overlap with arXiv:1312.4685 by other authors

References in corpus (1)

• Finitely Generated Nil but Not Nilpotent Evolution Algebra

Cited by in corpus (10)

• The algebraic and geometric classification of nilpotent Novikov algebras
• The algebraic and geometric classification of nilpotent bicommutative algebras
• Classification of bilinear maps with radical of codimension 2
• The classification of $n$-dimensional anticommutative algebras with $(n-3)$-dimensional annihilator
• Classification of asexual diploid organisms by means of strongly isotopic evolution algebras defined over any field
• A historical perspective of Tian's evolution algebras
• Central extensions of filiform associative algebras
• Determining when an algebra is an evolution algebra
• Algebraic computation of genetic patterns related to three-dimensional evolution algebras
• Five-dimensional nilpotent evolution algebras