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- W1997711254 abstract "Let A be a finite-dimensional oriented quantum algebra over a field k There an oriented quantum algebra structure on A⊗A which is motivated by an algebra isomorphism of the quantum double D(A) with A⊗A when A has a factorizable Hopf algebra structure. We describe and study the oriented quantum algebra structure on A⊗A and work it out in detail when A = M 2 (k) is the algebra of 2×2 matrices over k and has the oriented quantum algebra structure which gives rise to the Jones polynomial. The resulting 16×16 braiding matrix gives rise to a non-trivial ambient isotopy invariant of oriented links. Suppose that A is a finite-dimensional factorizable Hopf algebra over k and that the double D(A) has a ribbon element. Then the Hennings invariant of 3-manifolds is defined for D(A) and can be computed in a very natural way terms of an oriented quantum algebra structure on A⊗A. We supply details for future calculations which are developed in [2]." @default.
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- W1997711254 date "2007-09-01" @default.
- W1997711254 modified "2023-09-25" @default.
- W1997711254 title "ON THE TENSOR PRODUCT OF AN ORIENTED QUANTUM ALGEBRA WITH ITSELF" @default.
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- W1997711254 doi "https://doi.org/10.1142/s0218216507005580" @default.
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