TY - JOUR

T1 - From supersymmetry to quantum commutativity

AU - Cohen, Miriam

AU - Westreich, Sara

PY - 1994/8/15

Y1 - 1994/8/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0002006139&partnerID=8YFLogxK

U2 - 10.1006/jabr.1994.1217

DO - 10.1006/jabr.1994.1217

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AN - SCOPUS:0002006139

SN - 0021-8693

VL - 168

SP - 1

EP - 27

JO - Journal of Algebra

JF - Journal of Algebra

IS - 1

ER -