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- W2883760603 abstract "Let $A$ be the path algebra of a Dynkin quiver over a finite field, and let $C_1(mathscr{P})$ be the category of 1-cyclic complexes of projective $A$-modules. In the present paper, we give a PBW-basis and a minimal set of generators for the Hall algebra $H(C_1(mathscr{P}))$ of $C_1(mathscr{P})$. Using this PBW-basis, we firstly prove the degenerate Hall algebra of $C_1(mathscr{P})$ is the universal enveloping algebra of the Lie algebra spanned by all indecomposable objects. Secondly, we calculate the relations in the generators in $H(C_1(mathscr{P}))$, and obtain quantum Serre relations in a quotient of certain twisted version of $H(C_1(mathscr{P}))$. Moreover, we establish relations between the degenerate Hall algebra, twisted Hall algebra of $A$ and those of $C_1(mathscr{P})$, respectively." @default.
- W2883760603 created "2018-08-03" @default.
- W2883760603 creator A5062998633 @default.
- W2883760603 date "2018-07-28" @default.
- W2883760603 modified "2023-09-27" @default.
- W2883760603 title "Minimal generators of Hall algebras of 1-cyclic perfect complexes" @default.
- W2883760603 doi "https://doi.org/10.48550/arxiv.1807.10892" @default.
- W2883760603 hasPublicationYear "2018" @default.
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