Let G be a complex reductive algebraic group, g its Lie algebra and h a reductive subalgebra of g, n a positive integer. Consider the diagonal actions G : g, NG(h) : h . We study a relation between the algebra C[h]G and its subalgebra consisting of restrictions to h of elements of C[g].

We show that, if A is a finite-dimensional *-simple associative algebra with involution (over the field K of real or complex numbers) whose hermitian part H( A, * > is of degree > 3 over its center, if B is a unital algebra with involution over 06, and if (I.11 is an algebra norm on H( A @ B, * 1, then there exists an algebra norm on A @ B whose restriction to H(A @ B, *> is equivalent to 11 . ...

We study actions of “compact quantum groups” on “finite quantum spaces”. According to Woronowicz and to general C-algebra philosophy these correspond to certain coactions v : A → A ⊗ H . Here A is a finite dimensional C-algebra, and H is a certain special type of Hopf ∗-algebra. If v preserves a positive linear form φ : A → C, a version of Jones’ “basic construction” applies. This produces a ce...

We consider the permutation group algebra defined by Cameron and show that if the permutation group has no finite orbits, then no homogeneous element of degree one is a zero-divisor of the algebra. We proceed to make a conjecture which would show that the algebra is an integral domain if, in addition, the group is oligomorphic. We go on to show that this conjecture is true in certain special ca...

In this note, we generalize a result of [4] (see also [9]) and set the isomorphism between the iterated cross product algebra H∨#(H#A) and braided analog of an A-valued matrix algebra H∨⊗A⊗H for a Hopf algebra H in the braided category C and for an H-module algebra A. As a preliminary step, we prove the equivalence between categories of modules over both algebras and category whose objects are ...

We consider the permutation group algebra defined by Cameron and show that if the permutation group has no finite orbits, then no homogeneous element of degree one is a zero-divisor of the algebra. We proceed to make a conjecture which would show that the algebra is an integral domain if, in addition, the group is oligomorphic. We go on to show that this conjecture is true in certain special ca...

We construct the H-von Neumann regular radical for H-module algebras and show that it is an H-radical property. We obtain that the Jacobson radical of twisted graded algebra is a graded ideal. For twisted H-module algebra R, we also show that rj(R#σH) = rHj(R)#σH and the Jacobson radical of R is stable, when k is an algebraically closed field or there exists an algebraic closure F of k such tha...

Let $\mathcal H$ be the class of algebras verifying Han's conjecture. In this paper we analyse two types with aim providing an inductive step towards proof Firstly show that if algebra $\Lambda$ is triangular respect to a system non necessarily primitive idempotents, and at idempotents belong H$, then in H$. Secondly consider $2\times 2$ matrix algebra, on diagonal, projective bimodules corners...

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We introduced a braided Sweedler cohomology, which is adequate to work with the H-braided cleft extensions studied in [G-G1]. Introduction In [Sw] a cohomology theory H(H,A) for a commutative module algebra A over a cocommutative Hopf algebra H was introduced. This cohomology is related to those of groups an Lie algebras in the following sense. When H is a group algebra k[G], then H(H,A) is can...