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Cohomological Hall algebra of a symmetric quiver

✍ Scribed by Efimov, Alexander I.

Book ID
120164029
Publisher
Cambridge University Press
Year
2012
Tongue
English
Weight
375 KB
Volume
148
Category
Article
ISSN
0010-437X

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We show that it is possible to define reflection isomorphisms on the double of the (twisted) Hall algebra of a quiver. Combining these reflections with Fourier transform yields an alternative construction of Lusztig's braid group action on a quantum enveloping algebra.

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Let H H kQ be the Ringel᎐Hall algebra of affine quiver Q. All indecomposable Ž . representations of Q, which can be generated inside H H kQ by ''smaller'' represen-Ž . tations of Q, are classified; systems of minimal homogeneous generators of H H kQ are explicitly written out.