Letters in Mathematical Physics

, Volume 23, Issue 2, pp 133–141

Differential calculi on quantum vector spaces with Hecke-type relations

  • John C. Baez

DOI: 10.1007/BF00703726

Cite this article as:
Baez, J.C. Lett Math Phys (1991) 23: 133. doi:10.1007/BF00703726


From a vector spaceV equipped with a Yang-Baxter operatorR one may form the r-symmetric algebraSRV=TV/〈vwR(vw)〉, which is a quantum vector space in the sense of Manin, and the associated quantum matrix algebraMRV=T(End(V))/〈fgR(fg)R-1〉. In the case whenR satisfies a Hecke-type identityR2=(1−q)R+q, we construct a differential calculus ΩRV forSRV which agrees with that constructed by Pusz, Woronowicz, Wess, and Zumino whenR is essentially theR-matrix of GLq(n). Elements of ΩRV may be regarded as differential forms on the quantum vector spaceSRV. We show that ΩRV isMRV-covariant in the sense that there is a coaction Φ*: ΩRVMRV ⊗ ΩRV with Φ*d=(1 ⊗ d)Φ* extending the natural coaction Φ:SRVMRVSRV.

AMS subject classifications (1991)


Copyright information

© Kluwer Academic Publishers 1991

Authors and Affiliations

  • John C. Baez
    • 1
  1. 1.Department of MathematicsWellesley CollegeWellesleyUSA
  2. 2.University of California at RiversideRiversideUSA