From Supersymmetry to Quantum Commutativity
From Supersymmetry to Quantum Commutativity
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DOI：
10.1006/jabr.1994.1217
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发表时间：
1994-08
影响因子：
0.9
通讯作者：
Miriam Cohen;S. Westreich
中科院分区：
文献类型：
--
作者：
Miriam Cohen;S. Westreich
Abstract Let (H, R) be a quasitriangular Hopf algebra acting on an algebra A. We study a concept of A being quantum commutative with respect to (H, R). Superalgebras which are graded commutative (called sometimes commutative superalgebras) are shown to be examples of such an action. There is an analogous notion of quantum commutativity for comodule algebra. The quantum plane Cq[x, y] is an example, both under the coaction of quantum 2 × 2 matrices, and also in a more novel way at q a root of unity. If H is a cocommutative finite dimensional Hopf algebra and (D(H), R) its Drinfeld double we show that H is quantum commutative with respect to (D(H), R). We discuss further examples of such actions and coactions, and show that the category A # HMod resembles (for such actions) the category of modules over commutative rings.
