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Nil graded self-similar algebras
(EUROPEAN MATHEMATICAL SOC, 2010)
In [19], [24] we introduced a family of self-similar nil Lie algebras L over fields of prime characteristic p > 0 whose properties resemble those of Grigorchuk and Gupta-Sidki groups. The Lie algebra L is generated by two ...
An algorithm for associative bilinear forms
(2009)
We establish the equivalence between the problem of existence of associative bilinear forms and the problem of solvability in commutative power-associative finite-dimensional nil-algebras. We use the tensor product to find ...
Bruhat order and nil-Hecke algebras for Weyl groupoids
(World Scientific, 2018-09)
We introduce nil-Hecke algebras for Weyl groupoids. We describe a basis and some properties of these algebras which lead to a notion of Bruhat order for Weyl groupoids.
Nil restricted Lie algebras of oscillating intermediate growth
(Elsevier, 2021-12-15)
On the nilpotence of the multiplication operator in commutative right nil algebras
(2002)
We study conditions under which the identity ((xx)x)x = 0 in a commutative nonassociative algebra A implies Rx is nil-potent where Rx is the multiplication operator Rx(y) = xy for all y in A. The separate conditions that ...
On the nilpotence of the multiplication operator in commutative right nil algebras
(MARCEL DEKKER INC, 2002)
Some examples of nil Lie algebras
(EUROPEAN MATHEMATICAL SOC, 2008)
Generalizing Petrogradsky`s construction, we give examples of infinite-dimensional nil Lie algebras of finite Gelfand-Kirillov dimension over any field of positive characteristic.