**Author: Ana Prlić**

#### Glasnik Matematički, Vol. 52, No. 2 (2017), 275-288.

DOI: 10.3336/gm.52.2.07

**Abstract.** Let be the Lie group , with maximal compact subgroup . Let be the complexification of the Lie algebra of , and let be the universal enveloping algebra of . Let be the Cartan decomposition of , and the Clifford algebra of with respect to the trace form on . In this paper we give explicit generators of the algebra .

**2010 Mathematics Subject Classification.** 22E47, 22E46.

**Key words and phrases.** Lie group, Lie algebra, representation, Dirac operator, Dirac cohomology.