Triangulated categories and Kac-Moody algebras

By L. Peng, Jie Xiao. 2000

117 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/cdfb7a80c5b9c792d62382bd2e343fd980755945

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. O. Schiffmann
2. T. Bridgeland
3. Andrew Hubery
4. Bin Zhu
5. Valerio Toledano Laredo
6. Jie Xiao
7. M. Gorsky
8. B. Keller

In Geometry and Topology

1. O. Schiffmann
2. Valerio Toledano Laredo
3. T. Bridgeland
4. Andrew Hubery
5. Bin Zhu
6. Jie Xiao
7. B. Keller
8. Yukinobu Toda

In Statistical and Nonlinear Physics

1. O. Schiffmann
2. Andrew Hubery
3. T. Bridgeland
4. Bin Zhu
5. Valerio Toledano Laredo
6. Jie Xiao
7. Alexander Kuznetsov
8. B. Keller

Citations in the corpus

• From triangulated categories to Lie algebras: A theorem of Peng and Xiao (2005, methodology): “We call T finitary if each homomorphism group is finite and, given any element h of the Grothendieck group G of T , there exist only finitely many isomorphism classes of indecomposables [X ] (up to shift) with hX = h.”
• LECTURES ON HALL ALGEBRAS (2006, background): “ Π = Y E g(AE) (|E|−1) and let LC(A) be the Z-Lie subalgebra of Π generated by elements {[SE],[TSE]}, where Sagain runs over all simple objects of A. This is a free Z-module. Theorem 5.15 (Peng-Xiao, [PX2]). The Lie algebra LC(A)⊗Z C is isomorphic to the Kac-Moody algebra g′ associated to the quiver”
• Stability conditions and Stokes factors (2008, background): “derived category D = Db(A). To do this it would first be necessary to find a natural way to associate a Ringel–Hall Lie algebra g(D) to a derived category like D. Some progress on this has been made in [22, 23] but the construction there looks a little ad hoc. In particular it is not clear that the re”
• Noncommutative projective curves and quantum loop algebras (2002, background): “Recently, Y. Lin and L. Peng [LP] independently obtained another construction of the enveloping algebra of double-loop algebras of type D4, E6, E7, and E8 by considering the root category (as in [ PX ]) of certain tame algebras 3g (the tubular algebras).”
• Locally finite triangulated categories (2005, methodology): “The results there were used to construct Lie algebras in [16,17].”