相关论文: K^*(BG) rings for groups $G=G_{38},...,G_{41}$ of …

Let p be a prime and q=p^g. We show that the Grothendieck ring of finitely generated F_{q}[SL(2,F_{q})]-modules is naturally isomorphic to the quotient of the polynomial algebra Z[x] by the ideal generated by f^[g](x)-x, where…

Let $K$ be a number field with ring of integers $R$. Given a modulus $\mathfrak{m}$ for $K$ and a group $\Gamma$ of residues modulo $\mathfrak{m}$, we consider the semi-direct product $R\rtimes R_{\mathfrak{m},\Gamma}$ obtained by…

In this paper we prove that any strongly embedded subgroup of a K*-group G of finite Morley rank and odd type that does not interpret any bad field is solvable if its Pruefer 2-rank is at least 2. If the normal 2-rank of G is at least 3…

We compute the $K$-groups of the $C^{*}$-algebra of bounded operators generated by the Boutet de Monvel operators with classical SG-symbols of order (0,0) and type 0 on $\mathbb{R}_{+}^{n}$, as defined by Schrohe, Kapanadze and Schulze. In…

Let G=GL_n be the general linear group over an algebraically closed field k and let g=gl_n be its Lie algebra. Let U be the subgroup of G which consists of the upper unitriangular matrices. Let k[g] be the algebra of regular functions on…

This paper is a sequel to a paper by the same authors, where they defined $K$-groups of model-theoretic structures, and computed $K_1$ of free modules over PIDs. In this paper, we compute $K_1$ of a right $M_q(R)$-module $M$, where $R$ is a…

Let k be an arbitrary field of characteristic zero. In this paper we study quotients of k-rational conic bundles over projective line by finite groups of automorphisms. We construct smooth minimal models for such quotients. We show that any…

Let $G$ be the group scheme $SL_2$ defined over a noetherian ring $k$. If $G$ acts on a finitely generated commutative $k$-algebra $A$, then $H^*(G,A)$ is a finitely generated $k$-algebra.

We introduce S-modules, generalizing the notion of Krein $C^*$-modules, where a fixed unitary replaces the symmetry of Krein $C^*$-modules. The representation theory on S-modules is explored and for a given $*$-automorphism $\alpha$ on a…

We establish a novel connection between the central binomial coefficients $\binom{2n}{n}$ and Gould's sequence through the construction of a specialized multivariate polynomial quotient ring. Our ring structure is characterized by ideals…

By the classical result of Milnor and Novikov, the unitary cobordism ring is isomorphic to a graded polynomial ring with countably many generators: $\Omega^U_*\simeq \mathbb Z[a_1,a_2,\dots]$, ${\rm deg}(a_i)=2i$. In this paper we solve a…

A finite group $G$ is called a Schur group, if any Schur ring over $G$ is the transitivity module of a point stabilizer in a subgroup of $\sym(G)$ that contains all right translations. We complete a classification of abelian $2$-groups by…

We generalize a recent result of Clausen: For a number field with integers O, we compute the K-theory of locally compact O-modules. For the rational integers this recovers Clausen's result as a special case. Our method of proof is quite…

We consider groups G which have a cocompact, 3-manifold model for the classifying space \underline{E}G. We provide an algorithm for computing the rationalized equivariant K-homology of \underline{E}G. Under the additional hypothesis that…

Let G be a split simple group of type G_2 over a field k, and let g be its Lie algebra. Answering a question of Colliot-Th\'el\`ene, Kunyavski\u{i}, Popov, and Reichstein, we show that the function field k(g) is generated by algebraically…

The goal of this article is to show that five explicitly given transformations, a rotation, two screw Heisenberg rotations, a vertical translation and an involution generate the Euclidean Picard modular groups with coefficient in the…

We prove a formula for the structure constants of multiplication of equivariant Schubert classes in both equivariant cohomology and equivariant K-theory of Kac-Moody flag manifolds G/B. We introduce new operators whose coefficients compute…

Let k^[6] denote a polynomial ring in 6 variables over an algebraically closed field k of characteristic zero and consider the action of SL2(k) on k^[6] induced by the irreducible representation of SL2 of degree 5 (the binary quintic…

This article determines the structure of the group ring $\mathbb{Z}_nG$, where $G$ is a finite group and $\mathbb{Z}_n$ is the ring of integers modulo $n$, such that $n$ is relatively prime to the order of $G$. The decomposition of…

In this paper, the generating functions of Garvans so-called $k$-ranks are used, to define a family of mock Eisenstein series. The $k$-rank moments are then expressed as partition traces of these functions. We explore the modular properties…