文摘
Can one compute the exponential rate of growth of the ⁎-codimensions of a PI-algebra with involution ⁎ over a field of characteristic zero? It was shown in [2] that any such algebra A has the same ⁎-identities as the Grassmann envelope of a finite dimensional superalgebra with superinvolution B . Here, by exploiting this result we are able to provide an exact estimate of the exponential rate of growth class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869316302800&_mathId=si1.gif&_user=111111111&_pii=S0021869316302800&_rdoc=1&_issn=00218693&md5=15548f10ad2930bae31a8d63f7075750" title="Click to view the MathML source">exp⁎(A)class="mathContainer hidden">class="mathCode"> of any PI-algebra A with involution. It turns out that class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869316302800&_mathId=si1.gif&_user=111111111&_pii=S0021869316302800&_rdoc=1&_issn=00218693&md5=15548f10ad2930bae31a8d63f7075750" title="Click to view the MathML source">exp⁎(A)class="mathContainer hidden">class="mathCode"> is an integer and, in case the base field is algebraically closed, it coincides with the dimension of an admissible subalgebra of maximal dimension of B.