Let δ and ε be the inner derivations of UT m(F) induced by the unit matrices e 1m and e mm respectively. We study the differential polynomial identities of the algebra UT m(F) under the coupled action of δ and ε. We produce a basis of the differential identities, then we determine the S n-structure of their proper multilinear spaces and, for the minimal cases m = 2, 3, their exact differential codimension sequence.
$(\delta,\varepsilon)$-Differential Identities of $UT_m(F)$
Vincenzo Nardozza
2021-01-01
Abstract
Let δ and ε be the inner derivations of UT m(F) induced by the unit matrices e 1m and e mm respectively. We study the differential polynomial identities of the algebra UT m(F) under the coupled action of δ and ε. We produce a basis of the differential identities, then we determine the S n-structure of their proper multilinear spaces and, for the minimal cases m = 2, 3, their exact differential codimension sequence.File in questo prodotto:
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