Abstract
ABSTRACT This paper is devoted to some ring theoretic properties of the jordanian deformation of the algebra of regular functions on the matrices with coefficients in an algebraically closed field of characteristic zero, and of the associated factor algebra . We prove in particular that the prime spectrum of is the disjoint union of five components, each of which being homeomorphic to the spectrum of a commutative (possibly localised) polynomial ring. So we can give an explicit description of the prime spectrum of , and check that any prime factor of satisfies the Gelfand-Kirillov property. Then we study the automorphism groups of the algebras and and prove that they are generated by linear automorphisms and exponentials of locally nilpotent derivations.
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