Centers associated with the Borel subalgebra of the general linear Lie algebra

Original · EN

We consider a Borel subalgebra of the general linear algebra and its subalgebra which is a Borel subalgebra of the special linear algebra, over arbitrary field. Let ∈{, }. We establish here explicit realizations of the center Z() and semi-center Sz() of the enveloping algebra, the Poisson center S() and Poisson semi-center S() of the symmetric algebra. We describe their structure as commutative rings and establish isomorphisms Z() S(), Sz() S()