nLab face algebra

Idea

Face algebra is a generalization of a bialgebra whose main examples appear in a generalization of FRT construction motivated by solvable models of face type. It can be considered as a special kind of weak Hopf algebras, and a fortiori of bialgebroids.

Literature

It has been introduced in

• Takahiro Hayashi, Face algebras and their Drinfel′d doubles, Proc. Symp. Pure Math. 56, part 2 (1994) (ed. W. J. Haboush) 49–61 doi gBooks

American Mathematical Society

• Takahiro Hayashi, Face algebras I-A generalization of quantum group theory, J. Math. Soc. Japan 50:2 (1998) 293–315 doi

That they can be considered as a special case of $\times_R$-bialgebras is found in

• Peter Schauenburg, Face algebras are $\times_R$-bialgebras, in: Rings, Hopf Algebras, and Brauer Groups, CRC Press 1998

category: algebra