APPROXIMATELY BIPROJECTIVE BANACH ALGEBRAS AND NILPOTENT IDEALS

Derivations Into N-th Duals of Ideals of Banach Algebras

ENUMERATION OF ad-NILPOTENT b-IDEALS FOR SIMPLE LIE ALGEBRAS

We provide explicit formulas for the number of ad-nilpotent ideals of a Borel subalgebra of a complex simple Lie algebra having fixed class of nilpotence.

Invariant Prime Ideals in Quantizations of Nilpotent Lie Algebras

De Concini, Kac and Procesi defined a family of subalgebras U + of a quantized universal enveloping algebra Uq(g), associated to the elements of the corresponding Weyl group W . They are deformations of the universal enveloping algebras U(n+ ∩ Adw(n−)) where n± are the nilradicals of a pair of dual Borel subalgebras. Based on results of Gorelik and Joseph and an interpretation of U + as quantiz...

Principal Ideals and Semi-direct Products in Commutative Banach Algebras

We prove necessary conditions for a commutative Banach algebra to be the semidirect product of some subalgebra together with a speci ed principal ideal. x

On Identifying the Maximal Ideals in Banach Algebras

We consider the problem of identifying the maximal ideals of a Banach algebra S that is contained in a larger Banach algebra B. If S is dense in B in an appropriate sense and if the spectral radii in S and B are the same, then S and B have the same maximal ideals. The result is illustrated by two examples of Banach algebras S in which the density and spectral radius conditions are easily shown ...