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answered Deformation quantization of a closed Riemann surface with genus >1
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comment Norms on Clifford algebra (C^* norm)
Well, the map you mention is an isomorphism of $\ast$-algebras, and matrix algebras (and direct sums of matrix algebras) have a unique C$^\ast$-norm (the operator norm). Perhaps there is some way to interpret this norm intrinsically on the Clifford algebra; perhaps consider the operator norm of the Clifford algebra acting on itself by left multiplication.
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comment How to recognize a Hopf algebra?
For the sake of those reading this question (including me!), could you specify the sense in which you mean "regular"? It's a pretty overloaded term...
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accepted Software for noncommutative Groebner bases over rational function fields
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comment Software for noncommutative Groebner bases over rational function fields
I've seen that other question, but it didn't address the question of which base fields are allowed.