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Mathematics > Representation Theory

arXiv:2206.00406 (math)
[Submitted on 1 Jun 2022 (v1), last revised 17 Jun 2022 (this version, v2)]

Title:Some Identities in Quantum Torus Arising from Ringel-Hall Algebras

Authors:Jiuzhao Hua
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Abstract:We define two classes of representations of quivers over arbitrary fields, called monomorphic representations and epimorphic representations. We show that every representation has a unique maximal nilpotent subrepresentation and the associated quotient is always monomorphic, and every representation has a unique maximal epimorphic subrepresentation and the associated quotient is always nilpotent. The uniquenesses of such subrepresenations imply two identities in the Ringel-Hall algebra. By applying Reineke's integration map, we obtain two identities in the corresponding quantum torus.
Comments: 9 pages; correcting typos and simplifying notations
Subjects: Representation Theory (math.RT); Combinatorics (math.CO)
Cite as: arXiv:2206.00406 [math.RT]
  (or arXiv:2206.00406v2 [math.RT] for this version)
  https://doi.org/10.48550/arXiv.2206.00406

Submission history

From: Jiuzhao Hua [view email]
[v1] Wed, 1 Jun 2022 11:15:32 UTC (7 KB)
[v2] Fri, 17 Jun 2022 06:27:32 UTC (7 KB)
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