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