Let be a primitive root of unity of order . We introduce a family of finite-dimensional algebras over the complex numbers, such that is a subalgebra of if , and is a -cleft extension.
The simple -modules are highest weight modules, which admit a tensor product decomposition: the first factor is a simple -module and the second factor is a simple -module. This factorization resembles the corresponding Steinberg decomposition, and the family of algebras resembles the presentation of the algebra of distributions of SL as a filtration by finite-dimensional subalgebras.
Cite this article
Iván Ezequiel Angiono, A Quantum Version of the Algebra of Distributions of SL. Publ. Res. Inst. Math. Sci. 54 (2018), no. 1, pp. 141–161DOI 10.4171/PRIMS/54-1-5