In this paper we study G-extensions of real and complex representations of a closed normal subgroup H of a compact Lie group G when G/H is connected. The main result gives a necessary and sufficient condition for every complex irreducible H-module to extend to a G-module. In particular, we show that every complex Hmodule extends to a G-module if the fundamental group of G/H is torsion free. We ...

Medium lacking serum but supplemented with milk will support the growth of sparse cells in culture. Milk obtained within 8 h after the birth of a calf (day 1 colostrum) is the most effective in supporting proliferation. In mixed cultures of early-passage bovine embryonic kidney (BEK) or early-passage calf kidney (CK) cells, both epithelial cells and fibroblasts grow in Dulbecco's modified eagle...

in this paper we study the module contractibility ofbanach algebras and characterize them in terms the conceptssplitting and admissibility of short exact sequences. also weinvestigate module contractibility of banach algebras with theconcept of the module diagonal.

This paper describes the introduction of synchrotron-based macromolecular crystallography (MX) into an undergraduate laboratory class. An introductory 2 week experimental module on MX, consisting of four laboratory sessions and two classroom lectures, was incorporated into a senior-level biochemistry class focused on a survey of biochemical techniques, including the experimental characterizatio...

Let G be a finite group and k a fixed algebraically closed field of characteristic p>0 . If p is odd, let H(; be the subring of H*(G,k) consisting of elements of even degree; following [20-22] we take H~=H*(G,k) if p=2, though one could just as well use the subring of elements of even degree for all p. H a is a finitely generated commutative k-algebra [13], and we let Va denote its associated a...

Abstract. In this article, we study tensor product of Hilbert C∗-modules and Hilbert spaces. We show that if E is a Hilbert A-module and F is a Hilbert B-module, then tensor product of frames (orthonormal bases) for E and F produce frames (orthonormal bases) for Hilbert A⊗B-module E ⊗F , and we get more results. For Hilbert spaces H and K, we study tensor product of frames of subspaces for H an...

Let G be a compact Lie group. Set Λ• = H∗(G) and S • = H(BG). The coefficients are in R or C. Suppose G acts on a reasonable space X. In the paper [GKM] Goresky, Kottwitz and MacPherson established a duality between the ordinary cohomology which is a module over Λ• and equivariant cohomology which is a module over S • . This duality is on the level of chains, not on the level of cohomology. The...

Let A d be the complex polynomial ring in d variables. A contractive A d-module is Hilbert space H equipped with an A d action such that for any ξ 1 , ξ 2 ,. Such objects have been shown to be useful for modeling d-tuples of mutually commuting operators acting on a Hilbert space. An example is given by H 2 d , which is the Hilbert space of holomorphic functions on B d = {z ∈ C d : |z| ≤ 1} gene...

Consider a field k of characteristic p > 0, G(r) the r-th Frobenius kernel of a smooth algebraic group G, DG(r) the Drinfeld double of G(r), and M a finite dimensional DG(r)-module. We prove that the cohomology algebra H(DG(r), k) is finitely generated and that H(DG(r),M) is a finitely generated module over this cohomology algebra. We exhibit a finite map of algebras θr : H(G(r), k) ⊗ S(g) → H(...