Quantised $\mathfrak{sl}_2$-differential algebras

Andrey Krutov and Pavle Pandžić

Address:
Mathematical Institute of Charles University, Sokolovská 83, Prague, Czech Republic
Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia

E-mail: andrey.krutov@matfyz.cuni.cz     pandzic@math.hr

Abstract: We propose a definition of a quantised ${\mathfrak{sl}}_2$-differential algebra and show that the quantised exterior algebra (defined by Berenstein and Zwicknagl) and the quantised Clifford algebra (defined by the authors) of ${\mathfrak{sl}}_2$ are natural examples of such algebras.

AMSclassification: primary 16T20; secondary 81R50, 17B37.

Keywords: quantum group, Clifford algebra, quantised exterior algebra, \mathfrak{g}-differential algebra.

DOI: 10.5817/AM2024-5-351