Group of Isometries of the Lattice $$K_0(\mathbb P_n)$$

IF 0.6 4区数学 Q3 MATHEMATICS Mathematical Notes Pub Date : 2024-07-05 DOI:10.1134/s0001434624030222

I. S. Beldiev

引用次数: 0

Abstract

We study the isometry group of the Grothendieck group $K_0(\mathbb P_n)$ equipped with a bilinear asymmetric Euler form. We prove several properties of this group; in particular, we show that it is isomorphic to the direct product of $\mathbb Z/2\mathbb Z$ by the free Abelian group of rank $[(n+1)/2]$. We also explicitly calculate its generators for $n\le 6$.

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K_0(\mathbb P_n)$$ 的等距网格群

摘要我们研究了带有双线性不对称欧拉形式的 Grothendieck 群 $K_0(\mathbb P_n)$ 的等几何群。我们证明了这个群的几个性质；特别是，我们证明了它与秩为$[(n+1)/2]$的自由阿贝尔群的$\mathbb Z/2\mathbb Z$ 的直接积同构。我们还明确地计算了它的（[(n+1)/2]）生成器。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.