## Differential identities of finite dimensional algebras and polynomial growth of the codimensions. (arXiv:1812.08715v1 [math.RA])

Let \$A\$ be a finite dimensional algebra over a field \$F\$ of characteristic zero. If \$L\$ is a Lie algebra acting on \$A\$ by derivations, then such an action determines an action of its universal enveloping algebra \$U(L)\$. In this case we say that \$A\$ is an algebra with derivation or an \$L\$-algebra. Here we study the differential \$L\$-identities of \$A\$ and the corresponding differential codimensions, \$c_n^L (A)\$, when \$L\$ is a finite dimensional semisimple Lie algebra. We give a complete characterization of the corresponding ideal of differential identities in case the sequence \$c_n^L (A)\$, \$n=1,2,\dots\$, is polynomially bounded. Along the way we determine up to PI-equivalence the only finite dimensional \$L\$-algebra of almost polynomial growth. 查看全文>>