Andrew Hubery

Personal details

• Address: School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
• E-mail:
• Office: 10.17 Maths Satellite
• Telephone: +44 113 34 39246
• Fax: +44 113 34 34971
• Research Group: Algebra, Geometry and Integrable Systems, Department of Pure Mathematics
• Curriculum Vitae

Teaching

• Introduction to Geometry
• Algebras and Representations
• Commutative Algebra and Algebraic Geometry

• Previous Years

Tutorials:

• Mathematics 2
• Sets, Sequences and Series

Office Hours: Email to arrange a meeting

Blackboard VLE
Web for Faculty

Research Students

• Stefan Wolf Thesis: The Hall Algebra and the Composition Monoid, Completed May 2009
• Julia Sauter Started September 2009

Research interests

• Representation theory of quivers
  Here is a talk I gave on quiver Grassmannians and Hall polynomials.
  
• Ringel-Hall algebras and quantum groups
• Varieties and schemes of modules
• Cluster algebras and tilting theory

Ph.D. Thesis

• Quiver Representations respecting a quiver automorphism and a theorem of Kac pdf

List of publications

1. Quiver representations respecting a quiver automorphism: a generalisation of a theorem of Kac, J. London Math. Soc. 69 (2004) 79-96 pdf
2. The composition algebra and composition monoid of the Kronecker quiver, J. London Math. Soc. 72 (2005) 137-150 pdf
3. Symmetric functions and the centre of the Ringel-Hall algebras of a cyclic quiver, Math. Z. 251 (2005) 705-719 pdf
4. Yang, Dong, On defining ideals or subrings of Hall algebras. With an appendix by Andrew Hubery, Algebr. Represent. Theory 10 (2007) 619--629 pdf
5. Hall polynomials for affine quivers, Represent. Theory 14 (2010) 355-378 pdf
6. The cluster complex of an hereditary algebra, accepted by Algebras and Representation Theory pdf

Proceedings Articles

1. Representations of a quiver with automorphism: generalising a theorem of Kac, Fields Institute Communications 45 (2005) 187-200
2. From triangulated categories to Lie algebras: A theorem of Peng and Xiao, Trends in Representation Theory of Algebras and Related Topics (Querétaro, 2004), editors J. De la Peña and R. Bautista, Contemp. Math. 406, Amer. Math. Soc. (2006) 51-66 math.RT/0502403
3. Ringel-Hall algebras of cyclic quivers, Lectures during the Workshop of ICRA XIII, São Paulo, Brazil arXiv:0904.0180

Preprints

• Acyclic cluster algebras via Ringel-Hall algebras pdf
• Three presentations of quantum affine gl_n pdf

Lecture Notes

• Galois Theory Notes from my course on Galois theory.
• Ringel-Hall Algebras These are notes from a graduate course on Ringel-Hall algebras. We start with hereditary algebras, cover the basic theory of Ringel-Hall algebras and Green's Formula, prove necessary results about generalised Kac-Moody Lie algebras and their quantised enveloping algebras, and finally prove Kac's Theorem on the dimension vectors of indecomposable modules using character formulae.
• Derived Hall Algebras These are notes from the Workshop on Derived Categories at the CRM in Barcelona. We discuss B. Toën's derived Hall algebras, as well as L. Peng and J. Xiao's elementary proof of this result.
• Notes on the Octahedral Axiom These are self-contained notes proving the equivalence of various forms of the Octahedral Axiom for triangulated categories.
• Notes on Fibre Bundles These are notes on fibre bundles, developing enough theory to prove an equivalence of categories between G-Spaces and H-bundles over H/G whenever we have a principal bundle H → H/G