Ideal-simple semirings. I.
We study whether the projective and injective properties of left -modules can be implied to the special kind of left -modules, especially to the case of inverse polynomial modules and Laurent polynomial modules.
Let be a complex, semisimple Lie algebra, with an involutive automorphism and set , . We consider the differential operators, , on that are invariant under the action of the adjoint group of . Write for the differential of this action. Then we prove, for the class of symmetric pairs considered by Sekiguchi, that . An immediate consequence of this equality is the following result of Sekiguchi: Let be a real form of one of these symmetric pairs , and suppose that is a -invariant...
2000 Mathematics Subject Classification: 16R50, 16R10.The paper is a survey on involutions (anti-automorphisms of order two) of different kinds. Starting with the first systematic investigations on involutions of central simple algebras due to Albert the author emphasizes on their basic properties, the conditions on their existence and their correspondence with structural characteristics of the algebras. Focusing on matrix algebras a complete description of involutions of the first kind on Mn(F)...