The Functor $K_{0}^{\operatorname {gr}}$ is Full and only Weakly Faithful

نویسندگان

چکیده

The Graded Classification Conjecture states that the pointed $K_{0}^{\operatorname {gr}}$ -group is a complete invariant of Leavitt path algebras finite graphs when these are considered with their natural grading by $\mathbb {Z}$ . strong version this conjecture functor full and faithful on category graded homomorphisms modulo conjugations invertible elements zero components. We show for unital countable it (modulo specified conjugations) only in certain weaker sense.

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ژورنال

عنوان ژورنال: Algebras and Representation Theory

سال: 2023

ISSN: ['1386-923X', '1572-9079']

DOI: https://doi.org/10.1007/s10468-023-10199-w