- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 645848, 5 pages
On the Homomorphisms of the Lie Groups and
1Department of Mathematics, Faculty of Science and Letters, Istanbul Technical University, Maslak, 34469 Istanbul, Turkey
2Department of Mathematics, Faculty of Science and Letters, Okan University, 34959 Istanbul, Turkey
Received 14 February 2013; Revised 1 April 2013; Accepted 7 April 2013
Academic Editor: Nail Migranov
Copyright © 2013 Fatma Özdemir and Hasan Özekes. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- R. Howe, “On the role of the Heisenberg group in harmonic analysis,” Bulletin of the American Mathematical Society, vol. 3, no. 2, pp. 821–843, 1980.
- A. Korányi and H. M. Reimann, “Foundations for the theory of quasiconformal mappings on the Heisenberg group,” Advances in Mathematics, vol. 111, no. 1, pp. 1–87, 1995.
- D.-C. Chang and I. Markina, “Geometric analysis on quaternion -type groups,” The Journal of Geometric Analysis, vol. 16, no. 2, pp. 265–294, 2006.
- O. Calin, D.-C. Chang, and I. Markina, “SubRiemannian geometry on the sphere ,” Canadian Journal of Mathematics, vol. 61, no. 4, pp. 721–739, 2009.
- R. S. Strichartz, “Sub-Riemannian geometry,” Journal of Differential Geometry, vol. 24, no. 2, pp. 221–263, 1986, Correction to Journal of Differential Geometry, vol. 30, no. 2, pp. 595–596, 1989.
- A. Kaplan, “On the geometry of groups of Heisenberg type,” The Bulletin of the London Mathematical Society, vol. 15, no. 1, pp. 35–42, 1983.
- O. Calin, D. C. Chang, and P. C. Greiner, Heisenberg Group and Its Generalizations, AMS/IP Series in Advanced Math., International Press, Cambridge, Mass, USA, 2007.
- B. F. Schutz, Geometrical Methods of Mathematical Physics, Cambridge University Press, Cambridge, UK, 1980.
- M. Korbelář and J. Tolar, “Symmetries of the finite Heisenberg group for composite systems,” Journal of Physics A, vol. 43, no. 37, Article ID 375302, 15 pages, 2010.
- E. Binz and S. Pods, The Geometry of Heisenberg Groups with Applications in Signal Theory, Optics, Quantization, and Field Quantization, vol. 151 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, USA, 2008.
- B. C. Hall, Lie groups, Lie Algebras, and Representations: An Elementary Introduction, vol. 222 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 2003.
- J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, vol. 9 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 1972.
- W. Fulton and J. Harris, Representation Theory: A First Course, vol. 129 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 1991.
- D. Ellinas and J. Sobczyk, “Quantum Heisenberg group and algebra: contraction, left and right regular representations,” Journal of Mathematical Physics, vol. 36, no. 3, pp. 1404–1412, 1995.
- S. Semmes, “An introduction to Heisenberg groups in analysis and geometry,” Notices of the American Mathematical Society, vol. 50, no. 6, pp. 640–646, 2003.
- D. H. Sattinger and O. L. Weaver, Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics, vol. 61 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1986.
- F. W. Warner, Foundations of Differentiable Manifolds and Lie Groups, Scott, Foresman and Co., London, UK, 1971.
- R. Gilmore, Lie Groups, Lie Algebras and Their Applications, A Wiley-Interscience Publication, Wiley, New York, NY, USA, 1974.