6533b7d9fe1ef96bd126d609

RESEARCH PRODUCT

Growth of Differential Identities

Carla Rizzo

subject

Pure mathematicsPolynomialSequenceLie algebraStructure (category theory)Triangular matrixUniversal enveloping algebraAssociative propertyDifferential (mathematics)Mathematics

description

In this paper we study the growth of the differential identities of some algebras with derivations, i.e., associative algebras where a Lie algebra L (and its universal enveloping algebra U(L)) acts on them by derivations. In particular, we study in detail the differential identities and the cocharacter sequences of some algebras whose sequence of differential codimensions has polynomial growth. Moreover, we shall give a complete description of the differential identities of the algebra UT2 of 2 × 2 upper triangular matrices endowed with all possible action of a Lie algebra by derivations. Finally, we present the structure of the differential identities of the infinite dimensional Grassmann G with respect to the action of a finite dimensional Lie algebra L of inner derivations.

yearjournalcountryeditionlanguage
2020-11-27
https://doi.org/10.1007/978-3-030-63111-6_20