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The left and right dimensions of a skew field over the subfield of invariants. (English) Zbl 06715050
Summary: If \(H\) is a Hopf algebra and \(A\) an \(H\)-module algebra without nontrivial \(H\)-stable left or right ideals, then the subalgebra of \(H\)-invariant elements \(A^H\) is a skew field and \(A\) may be regarded as a vector space over \(A^H\) with respect to either left or right multiplications. It is proved in the paper that the left dimension of \(A\) over \(A^H\) is equal to the right dimension under the assumptions that \(A\) is semiprimary and \(\dim H < \infty\). In the case when \(A\) is itself a skew field, this answers a question raised by J. Bergen, M. Cohen and D. Fischman.
16T05 Hopf algebras and their applications
Full Text: DOI
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