Abstract
It is known that Green’s formula over finite fields gives rise to the comultiplications of Ringel–Hall algebras and quantum groups (see [Invent. Math. 120 (1995), 361–377], see also [J. Amer. Math. Soc. 4 (1991), 365–421]). In this chapter, we prove a projective version of Green’s formula in a geometric way. Then following the method of Hubery in [Hubery, Acyclic cluster algebras via Ringel–Hall algebras (preprint)], we apply this formula to proving Caldero–Keller’s multiplication formula for acyclic cluster algebras of arbitrary type.
Mathematics Subject Classifications (2000): 14M99, 16G20, 16G70, 17B35
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Xiao, J., Xu, F. (2010). Green’s Formula with ℂ*-Action and Caldero–Keller’s Formula for Cluster Algebras. In: Gyoja, A., Nakajima, H., Shinoda, Ki., Shoji, T., Tanisaki, T. (eds) Representation Theory of Algebraic Groups and Quantum Groups. Progress in Mathematics, vol 284. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4697-4_13
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DOI: https://doi.org/10.1007/978-0-8176-4697-4_13
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