Cohomology rings for quantized enveloping algebras

Abstract

Abstract. We compute the structure of the cohomology ring for the quantized enveloping algebra (quantum group) Uq associated to a finite-dimensional simple complex Lie algebra g. We show that the cohomology ring is generated as an exterior algebra by homogeneous elements in the same odd degrees as generate the cohomology ring for the Lie algebra g. Partial results are also obtained for the cohomology rings of the non-restricted quantum groups obtained from Uq by specializing the parameter q to a non-zero value ε ∈ C.

A characteristic map for compact quantum groups

“…We finally note that along the way to compute the Hochschild (co)homology of U q (g), regarded as an algebra, the Tor-groups Tor Uq(g) * (k, k) and the Ext-groups Ext * Uq(g) (k, k) are obtained in [10].…”

Contradictions in the Discourse of Imperialism with a Focus on Writings by Western Visitors to Korea

“…The quantum Borcherds-Bozec algebras were introduced by T. Bozec [1] in his study of perverse sheaves on arbitrary quiver representation varieties, possibly with loops. He showed that the Grothendieck group arising from Lusztig sheaves is generated by the elementary simple perverse sheaves, answering a question posed by Lusztig in [12].…”