K-theory for Leavitt path algebras: Computation and classification

JOURNAL OF ALGEBRA

卷:433

Article

Gabe, James¹  Ruiz, Efren²  Tomforde, Mark³  Whalen, Tristan³ 

[1] Univ Copenhagen, Dept Math Sci, DK-2100 Copenhagen, Denmark

[2] Univ Hawaii, Dept Math, Hilo, HI 96720 USA

[3] Univ Houston, Dept Math, Houston, TX 77204 USA

关键词: Leavitt path algebra;    Algebraic K-theory;    Morita equivalence;    Classification;    Number field;   

DOI  :  10.1016/j.jalgebra.2015.03.009

来源: Elsevier

【 摘 要 】

We show that the long exact sequence for K-groups of Leavitt path algebras deduced by Ara, Brustenga, and Cortifias extends to Leavitt path algebras of countable graphs with infinite emitters in the obvious way. Using this long exact sequence, we compute explicit formulas for the higher algebraic K-groups of Leavitt path algebras over certain fields, including all finite fields and all algebraically closed fields. We also examine classification of Leavitt path algebras using K-theory. It is known that the K-0-group and K-1-group do not suffice to classify purely infinite simple unital Leavitt path algebras of infinite graphs up to Morita equivalence when the underlying field is the rational numbers. We prove for these Leavitt path algebras, if the underlying field is a number field (which includes the case when the field is the rational numbers), then the pair consisting of the K-0-group and the K-6-group does suffice to classify these Leavitt path algebras up to Morita equivalence. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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