Fields of fractions of quantum solvable algebras
نویسنده
چکیده
Consider a field k of characteristic zero. Let Q = (qij) be a n× n-matrix with the entries qij ∈ k∗ or qij is an indeterminate, satisfying qijqji = qii = 1. The algebra k[Q] is generated by k and q ij , i, j = 1, . . . , n. Denote k(Q) = Fract(k[Q]) and Γ is the subgroup in k(Q) generated by k and the entries of Q. Throughout the paper R is a k-algebra with a unit. Definition 1.1. We say that R is a Q-algebra if k[Q] is contained in the center of R (i.e. R is a k[Q]-module). Definition 1.2. An algebra R is Q-solvable if R is a Q-algebra and it is generated by the elements x1, x2, . . . , xn over k[Q] with the defining relations
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