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arXiv · 1610.01825

$K$-theory of monoid algebras and a question of Gubeladze

Amalendu Krishna·Husney Parvez Sarwar
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Abstract

We show that for any commutative noetherian regular ring $R$ containing $\Q$, the map $K_1(R) \to K_1(\frac{R[x_1, \cdots , x_4]}{(x_1x_2 - x_3x_4)})$ is an isomorphism. This answers a question of Gubeladze. We also compute the higher $K$-theory of this monoid algebra. In particular, we show that the above isomorphism does not extend to all higher $K$-groups. We give applications to a question of Lindel on the Serre dimension of monoid algebras.

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Amalendu Krishna, Husney Parvez Sarwar. 2016-10-06. $K$-theory of monoid algebras and a question of Gubeladze. https://doi.org/10.1017/s1474748017000317

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