Hopf algebras and vector symmetries. (English. Russian original) Zbl 0649.16008

Lyubashenko, V. V.

Russ. Math. Surv. 41, No. 5, 153-154 (1986); translation from Usp. Mat. Nauk 41, No. 5(251), 185-186 (1986).

From a given solution of the Yang-Baxter equation with special properties we construct tensor categories. In these we can consider an analogue of \({\mathbb{Z}}/2\)-graded analysis, generalizing results of R. Trostel [Hadronic J. 6, 1518-1578 (1983; Zbl 0559.58003)].

MSC:

16W30	Hopf algebras (associative rings and algebras) (MSC2000)
58A10	Differential forms in global analysis
81S05	Commutation relations and statistics as related to quantum mechanics (general)
16B50	Category-theoretic methods and results in associative algebras (except as in 16D90)
16W50	Graded rings and modules (associative rings and algebras)

Keywords:

Yang-Baxter equation; tensor categories; \({bbfZ}/2\)-graded analysis

Citations:

Zbl 0559.58003