engleski

Computation of constants in multiparametric algebras of noncommutative polynomials

Let N be a fixed subset of the set of nonnegative integers. Then we denote by B the free unital associative C-algebra with N generators, each of degree one. We can think of B as an algebra of noncommutative polynomials in n noncommuting variables ei1, ..., ein. We equip B with a multiparametric qij-differential structure given by n linear operators ∂i:B→B, i∈N that act as twisted derivations on B. The algebra B is naturally graded by total degreere. More generally we also have a finer decomposition of B into multigraded components i.e. weight subspaces BQ. Of particular interest in algebra B are elements called constants. An element in B is called a constant if it is annihilated by operators ∂i. Let C denotes the space of all constants in algebra B and similarly let CQ denotes the space of all constants in BQ. Then the main problem of describing the space C can be reduced to describing the space CQ.

q-algebras; noncommutative polynomial algebras; twisted derivations

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