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pro vyhledávání: '"Mirzaii, Behrooz"'
Autor:
Mirzaii, Behrooz, Pérez, Elvis Torres
In this article we study the first, the second and the third homology groups of the elementary group $\textrm{E}_2(A)$, where $A$ is a commutative ring. In particular, we prove a refined Bloch-Wigner type exact sequence over a semilocal ring (with so
Externí odkaz:
http://arxiv.org/abs/2407.17632
Autor:
Mirzaii, Behrooz, Pérez, Elvis Torres
In this article we study the low dimensional homology of the projective linear group $\textrm{PGL}_2(A)$ over a commutative ring $A$. In particular, we prove a Bloch-Wigner type exact sequence over local domains. As applications we prove that $H_2(\t
Externí odkaz:
http://arxiv.org/abs/2405.08950
Autor:
Mirzaii, Behrooz, Pérez, Elvis Torres
In this article we study the low dimensional homology groups of the special linear group $\textrm{SL}_2(A)$ and the projective special linear group $\textrm{PSL}_2(A)$, $A$ a domain, through the natural surjective map $\textrm{SL}_2(A) \to \textrm{PS
Externí odkaz:
http://arxiv.org/abs/2402.08074
Autor:
Mirzaii, Behrooz, Pérez, Elvis Torres
For an arbitrary ring $A$, we study the abelianization of the elementary group $\textrm{E}_2(A)$. In particular, we show that for a commutative ring $A$ there exists an exact sequence \[ K_2(2,A)/C(2,A) \to A/M \to \textrm{E}_2(A)^\textrm{ab} \to 1,
Externí odkaz:
http://arxiv.org/abs/2401.06330
Autor:
Mirzaii, Behrooz, Pérez, Elvis Torres
In this paper we investigate the third homology of the projective special linear group $\textrm{PSL}_2(A)$. As a result of our investigation we prove a projective refined Bloch-Wigner exact sequence over certain class of rings. The projective Bloch-W
Externí odkaz:
http://arxiv.org/abs/2401.04341
Autor:
Mirzaii, Behrooz, Pérez, Elvis Torres
There is a natural connection between the third homology of $\textrm{SL}_2(A)$ and the refined Bloch group $\mathcal{RB}(A)$ of a commutative ring $A$. In this article we investigate this connection and as the main result we show that if $A$ is a uni
Externí odkaz:
http://arxiv.org/abs/2307.08872
Autor:
Mirzaii, Behrooz, Pérez, Elvis Torres
Let $A$ be a local domain of characteristic $2$ such that its residue field has more than $64$ elements. Then we find an exact relation between the third integral homology of the group $\mathrm{SL}_2(A)$ and Hutchinson's refined Bloch group $\mathcal
Externí odkaz:
http://arxiv.org/abs/2304.07443
Autor:
Mirzaii, Behrooz, Torres Pérez, Elvis
Publikováno v:
In Journal of Algebra 1 November 2024 657:141-158
Autor:
Mirzaii, Behrooz, Torres Pérez, Elvis
Publikováno v:
In Journal of Pure and Applied Algebra June 2024 228(6)
Autor:
Mirzaii, Behrooz
For an infinite field $F$, we study the kernel of the map $H_{n}(\mathrm{GL}_{n-1}(F),\mathbb{Z}\Big[\frac{1}{(m-2)!}\Big]) \to H_{n}(\mathrm{GL}_{n}(F),\mathbb{Z}\Big[\frac{1}{(m-2)!}\Big])$ and the cokernel of $H_{n+1}\Big(\mathrm{GL}_{n-1}(F),\mat
Externí odkaz:
http://arxiv.org/abs/2011.03820