DOI QR코드

DOI QR Code

Quantum Super Theta Vectors and Theta Functions

  • Kim, Hoil (Department of Mathematics, Kyungpook National University)
  • Received : 2016.01.18
  • Accepted : 2016.02.05
  • Published : 2016.03.23

Abstract

There are many concepts around classical theta functions, theta vectors and quantum theta functions. Manin clarified the relation among these concepts with the symmetry of functional equations. We extend his results to the super torus.

Keywords

Acknowledgement

Supported by : National Research Foundation of Korea (NRF)

References

  1. A. Connes, M. Douglas and A. Schwarz, Noncommutative geometry and matrix theory: Compactification on tori, JHEP, 9802:003(1998).
  2. C. Ee, H. Kim and H. Nakajima, Noncommutative superspace and super Heisenberg group, JHEP, 0804:004(2008).
  3. C. Ee, H. Kim and H. Nakajima, Noncommutative supertori in two dimensions, JHEP, 0808:058(2008).
  4. Y. Manin, Functional equations for quantum theta functions, Publ. Res. Inst. Math. Sci. Kyoto, 40(3)(2004), 605-624.
  5. Y. Manin, Theta functions, quantum tori and Heisenberg Groups, Lett. Math. Phys., 56(3)(2001), 295-320. https://doi.org/10.1023/A:1017909525397
  6. D. Mumford (with M. Nori and P. Norman), Tata Lectures on Theta III, Progress in Math., Vol. 97, Birkhauser, 1991.
  7. D. Quillen, Superconnections and the Chern character, Topology, 24(1)(1985), 89-95. https://doi.org/10.1016/0040-9383(85)90028-X
  8. M. Rieffel, Projective modules over higher dimensional noncommutative tori, Can. J. Math., 40(2)(1988), 257-338. https://doi.org/10.4153/CJM-1988-012-9
  9. A. Schwarz, Theta functions on non-commutative tori, Lett. Math. Phys., 58(2001), 81-90. https://doi.org/10.1023/A:1012515417396