On Constructing Ideals of the Hall Algebra of Type B
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Type B
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Let Hv(An) and Hv(Bn) be the Hall algebras over ℚ(v) of the Dynkin quivers An and Bn (n ≥ 1), respectively, where v is an indeterminate and the quivers have linear orientation. By comparing the quantum Serre relations, we find a natural algebra epimorphism π : Hv(Bn) → Hv2(An). We determine the kernel of π by giving two sets of generators. Let φ be the natural algebra homomorphism from Hv(An) to the quantized Schur algebra Sv(n + 1, r)(r ≥ 1) and write [Formula: see text] for the induced map. We obtain several ideals of Hv(Bn) by lifting the kernel of φ to the kernel of the composition map [Formula: see text].
2019 ◽
Vol 150
(3)
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pp. 1581-1607
2017 ◽
Vol 20
(02)
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pp. 1750013
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2018 ◽
Vol 2020
(15)
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pp. 4721-4775
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2018 ◽
Vol 19
(3)
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pp. 971-1028
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2013 ◽
Vol 149
(6)
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pp. 914-958
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2020 ◽
Vol 2020
(760)
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pp. 59-132
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