My main area of research is Algebra. In particular, I
am
interested in the following:
- 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
D-modules.
Preprints on the arxiv.
- Anti-Yetter-Drinfeld modules for quasi-Hopf algebras, (with I. Kobyzev), SIGMA: Symmetry Integrability Geom. Methods Appl., 14 (2018), 098, 10 pages.
- A categorical approach to cyclic cohomology of quasi-Hopf algebras and Hopf algebroids, (with I. Kobyzev), Appl. Categ. Structures, doi.org/10.1007/s10485-018-9544-0.
- Extensions and duality, 16 pages.
- On the anti-Yetter-Drinfeld module-contramodule correspondence, to appear in J. Noncommut. Geom., 32 pages.
- Some invariance properties of cyclic cohomology with coefficients, 29 pages.
- Monoidal Categories, 2-Traces, and Cyclic Cohomology (with M. Hassanzadeh, M. Khalkhali), Canad. Math. Bull., doi.org/10.4153/CMB-2018-016-4.
- Cyclic homology
for Hom-associative algebras (with M. Hassanzadeh, S. Sutlu), J. Geom. Phys., Volume 98 (2015),
40-56.
- 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.
- Twisted
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.
- $p$-adic
superspaces and Frobenius (with A. Schwarz), Communications in Mathematical
Physics, Volume 282 (2008), Number 1, p. 87–113.
- Gelfand-Fuchs
cohomology of invariant formal vector fields (with X. Tang), Mathematical
Research Letters Volume 15 (2008), Number 1, p. 129–149.
- Supergeometry
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.