Cocycle Deformations of Algebraic Identities and R-matrices

Abstract

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.

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