First cohomology groups of finite groups with nontrivial irreducible coefficients have been useful in several geometric and arithmetic contexts, including Wiles’s famous paper (1995). Internal to group theory, 1-cohomology plays a role in the general theory of maximal subgroups of finite groups, as developed by Aschbacher and Scott (1985).One can pass to the case where the group acts faithfully...

If G is a locally compact groupoid with a Haar system λ, then a positive definite function p on G has a form p(x) = 〈L(x)ξ(d(x)), ξ(r(x))〉, where L is a representation of G on a Hilbert bundle H = (G, {Hu}, μ), μ is a quasi invariant measure on G 0 and ξ ∈ L(G,H). [10]. In this paper firt we prove that if μ is a quasi invariant ergodic measure on G, then two corresponding representations of G a...

We compute the Yoneda extension algebra of GL2 over an algebraically closed field of characteristic p > 0. 1. Intro Let F be an algebraically closed field of characteristic p > 0. Let G = GL2(F ) denote the group of 2 × 2 invertible matrices over F . Let L denote a complete set of irreducible objects in the category G -mod of rational representations of G. The object of this paper is to give an...

The “main conjecture” of equivariant Iwasawa theory concerns the situation where • l is a fixed odd prime number and K/k is a Galois extension of totally real number fields with k/Q and K/k∞ finite, where k∞/k is the cyclotomic Zl-extension (we set G = G(K/k) and Γk = G(k∞/k)), • S is a fixed finite set (which will normally be suppressed in the notation) of primes of k containing all primes whi...

The “main conjecture” of equivariant Iwasawa theory concerns the situation where • l is a fixed odd prime number and K/k is a Galois extension of totally real number fields with k/Q and K/k∞ finite, where k∞/k is the cyclotomic Zl-extension (we set G = G(K/k) and Γk = G(k∞/k)), • S is a fixed finite set (which will normally be suppressed in the notation) of primes of k containing all primes whi...

Scenario according to which the SU(2)-gluodynamics is a theory with a nontrivial fixed point is analyzed from the point of view of the modern Monte-Carlo (MC) lattice data. It is found that an assumption of the first order fixed point g = g f of the beta function β f (g) has no contradictions with existing MC lattice data. The beta function parameters are found from the requirement of constant ...

for each f, g ∈ L (G). For the theory of this Banach algebra, see [8], [14], [17], and [2, §3.3], for example. There are many standard left (and right) Banach L(G)-modules. Here we determine when these modules have certain well-known homological properties; we shall summarize some known results, and establish various new ones. In fact, we are seeking to characterize the locally compact groups G...

In this work we investigate bounded Lukasiewicz logics, characterised as the intersection of the k-valued Lukasiewicz logics for k = 2, . . . , n (n ≥ 2). These logics formalise a generalisation of Ulam’s game with applications in Information Theory. Here we provide an analytic proof calculus G LBn for each bounded Lukasiewicz logic, obtained by adding a single rule to G L, a hypersequent calcu...