arXiv subjects

Aura-Cristiana Radu

Publications and source records attributed to Aura-Cristiana Radu.

2 recordsLinked to original sources

arXiv2024

C*-algebras of higher-rank graphs from groups acting on buildings, and explicit computation of their K-theory

We unite elements of category theory, K-theory, and geometric group theory, by defining a class of groups called $k$-cube groups, which act freely and transitively on the product of $k$ trees, for arbitrary $k$. The quotient of this action on the product of trees defines a $k$-dimensional cube complex, which induces a higher-rank graph. We make deductions about the K-theory of the corresponding $k$-rank graph C*-algebras, and give explicit examples of $k$-cube groups and their K-theory. We give explicit computations of K-theory for an infinite family of $k$-rank graphs for $k\geq 3$, which is not a direct consequence of the Künneth Theorem for tensor products.

math.OA↗

arXiv2021

On the cohomology of the Ree groups and kernels of exceptional isogenies

Let $G$ be a simple, simply connected algebraic group over an algebraically closed field $k$ of characteristic $p>0$. Let $σ: G \rightarrow G$ be a surjective endomorphism of $G$ such that the fixed point set $G(σ)$ is a Suzuki or Ree group. Then, let $G_σ$ denote the scheme-theoretic kernel of $σ.$ Using methods of Jantzen and Bendel-Nakano-Pillen, we compute the $1$-cohomology for the Frobenius kernels with coefficients in the induced modules, $H^{1}(G_σ, H^{0}(λ))$, and the $1$-cohomology for the Frobenius kernels with coefficients in the simple modules, $H^{1}(G_σ, L(λ))$ for the Suzuki and Ree groups. Moreover, we improve the known bounds for identifying extensions for the Ree groups of type $F_4$ with the ones for the algebraic group.

math.RT↗