Journal of Lie Theory

no. 2
Uq(sl(m+1))-Module Algebra Structures on the Coordinate Algebra of a Quantum Vector Space
Journal of Lie Theory, Volume 25 (2015) no. 2, pp. 327-361
We study the module-algebra structures of $U_q(sl(m+1))= {\cal H}(e_i,f_i,k_i^{\pm1})_{1\leq i\leq m}$ on the coordinate algebra of quantum vector spaces are studied. We denote the coordinate algebra of quantum $n$-dimensional vector space by $A_q(n)$. As our main result, first, we give a complete classification of module-algebra structures of $U_q(sl(m+1))$ on $A_q(3)$ when $k_i\in {\rm Aut L}(A_q(3))$ as actions on $A_q(3)$ for $i=1,\cdots, m$ and $m\geq 2$ and with the same method, on $A_q(2)$, all module-algebra structures of $U_q(sl(m+1))$ are characterized. Lastly, the module-algebra structures of $U_q(sl(m+1))$ on $A_q(n)$ are obtained for any $n\geq 4$.
DOI: 10.5802/jolt.839
Classification: 81R50, 16T20, 17B37, 20G42, 16S40
Keywords: Quantum enveloping algebra, coordinate algebra of quantum vector space, Hopf action, module algebra, weight 
@article{JOLT_2015_25_2_a1,
     author = {S. Duplij and Y. Hong and F. Li},
     title = {U\protect\textsubscript{q}(sl(m+1))-Module {Algebra} {Structures} on the {Coordinate} {Algebra} of a {Quantum} {Vector} {Space}},
     journal = {Journal of Lie Theory},
     pages = {327--361},
     year = {2015},
     volume = {25},
     number = {2},
     doi = {10.5802/jolt.839},
     zbl = {1332.81094},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.839/}
}
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S. Duplij; Y. Hong; F. Li. Uq(sl(m+1))-Module Algebra Structures on the Coordinate Algebra of a Quantum Vector Space. Journal of Lie Theory, Volume 25 (2015) no. 2, pp. 327-361. doi: 10.5802/jolt.839

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