My main area of research is Algebra. In particular, I
interested in the following:
Preprints on the arxiv.
- Hopf algebras, weak Hopf algebras.
- Fusion categories, monoidal categories, dualities.
- Homological algebra, Cyclic homology.
- Frobenius actions on cohomology.
- Hom-associative algebras.
- Lie algebras and their cohomology.
- Orbifold invariants.
- Groups with symplectic self-duality.
- Representations of affine Kac-Moody Lie algebras arizing from
- A categorical approach to cyclic cohomology of quasi-Hopf algebras and Hopf algebroids, (with I. Kobyzev), 25 pages.
- Extensions and duality, 16 pages.
- On the anti-Yetter-Drinfeld module-contramodule correspondence, 32 pages.
- Some invariance properties of cyclic cohomology with coefficients, 29 pages.
- Monoidal Categories, 2-Traces, and Cyclic Cohomology (with M. Hassanzadeh, M. Khalkhali), 17 pages.
- Cyclic homology
for Hom-associative algebras (with M. Hassanzadeh, S. Sutlu), J. Geom. Phys., Volume 98 (2015),
- On the relative
dual of an $S^1$-gerbe over an orbifold (with X. Tang, H. Tseng), Advances
in Mathematics 270 (2015), 1-20.
- Frobenius map and
the $p$-adic Gamma function, Journal
of Number Theory, Volume 132,
Issue 8, (2012), 1770–1779.
- Locally compact
abelian groups with symplectic self-duality (with A. Prasad, M. K.
Vemuri), Advances in Mathematics
225 (2010), no. 5, 2429–2454.
- Frobenius map for
quintic threefolds, International
Mathematics Research Notices (2009),
Volume 2009, Number 13, 2519–2545.
- Frobenius map on
local Calabi-Yau manifolds, Journal
of Mathematical Physics 50 (2009),
no. 2, 022302, 14 pp.
- The BRST
reduction of the chiral Hecke algebra, Advances in Mathematics 220 (2009),
no. 6, 1657–1688.
de Rham cohomology, homological definition of the integral and "Physics
over a ring" (with A. Schwarz), Nuclear
Physics B, Volume 809 (2009), no. 3, p. 547–560.
superspaces and Frobenius (with A. Schwarz), Communications in Mathematical
Physics, Volume 282 (2008), Number 1, p. 87–113.
cohomology of invariant formal vector fields (with X. Tang), Mathematical
Research Letters Volume 15 (2008), Number 1, p. 129–149.
and Arithmetic Geometry (with A. Schwarz), Nuclear Physics B, Volume
756 (2006), Issue 3, p. 207–218.
- Some remarks
on Gopakumar-Vafa invariants (with A. Schwarz), Pure and Applied Mathematics
Quarterly Vol 1 (2005), Number 4, p. 817–826.