Cocycle Deformations of Algebraic Identities and R-matrices

Details Cocycle Deformations of Algebraic Identities and R-matrices Cocycle Deformations of Algebraic Identities and R-matrices

2008-02-15

arxiv.org/abs/0802.2294v1

Mathematics

Geometric Topology

17 pages, 15 figures, submitted to the Quantum Topology Hanoi Conference Proceedings

Scientific paper

For an arbitrary identity L=R between compositions of maps L and R on tensors of vector spaces V, a general construction of a 2-cocycle condition is given. These 2-cocycles correspond to those obtained in deformation theories of algebras. The construction is applied to a canceling pairings and copairings, with explicit examples with calculations. Relations to the Kauffman bracket and knot invariants are discussed.

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