Generalized groupoid morphisms

Grant CEEX from the Romanian Ministry of Education and Research
Code ET 65/2005 (Excellence research projects for young researchers), contract no. 2987/11.10.2005
Project manager: Mădălina Roxana Buneci (assoc. professor, UCB)
Research team: Novac Claudiu Chiriac (lecturer, UCB), Dragoş Pătru Covei (assist. lecturer, UCB), Sorin-Mirel Stoian (lecturer dr., Univesity of Petroşani)


Abstract

The aim of this project is to generalize the notion of groupoid morphism. We shall introduced these morphisms (in a generalized sense) in order to obtain functorial maps from the categories of groupoids (endowed with various structures) as objects and our morphisms as arrows (morphisms) to a suitable categories of C*-algebras. There is a high potential for applications in noncommutative geometry and physics.

Reports

• 2005-report (in Romanian)
• 2006-report (in Romanian)
• 2007-report (in Romanian)
• Final report (in Romanian)

List of papers that are (partially) supported by this grant

• M. Buneci, Morphisms of discrete dynamical systems, Discrete and Continuous Dynamical Systems, 29 (1) (2011), 91-107. [ISSN 1078-0947].

M. Buneci, Topological groupoids with locally compact fibres, Topology Proceedings, 37 (2011), 239-258. [ISSN 0146-4124].

• M. Stoian, A Functional Calculus for Quotient Bounded Operators, International Conference on Infinite Dimensional Analysis (Function Theory on Infinite Dimensional Spaces X), Universidad Complutense, Madrid, December 11-14, 2007.

• M. Stoian, Quasi-nilpotent operators on locally convex spaces, arXiv: math.FA/0708.1819.

• M. Buneci, Groupoids and actions, The 4th International Scientific Conference ECO-TREND 2007, November 23-24, Targu-Jiu, Romania.

• M. Buneci, A category of singly generated dynamical systems, International Conference on Dynamical Systems (2007), Editors Cenap Ozel and Veli Cay, International Academic Press, 122-129.

• D. Covei, Entire solution of quasilinear elliptic problem, submitted for publication.

• N. Chiriac, The principle of the minimum action in true time, The 12th edition of the International Scientific Conference of the Engineering Faculty, November 23rd-24th, 2007. Nr.3/2007, 219-222. [ISSN: 1842-4856]

• M. Buneci, C*-Norms on the Algebra of Continuous Functions with Compact Support on a Locally Compact Groupoid, An. Univ. Timisoara Ser. Mat.-Inform. 45(2007) no. 1, 91-108. [ISSN 1224-970X].

• M. Buneci, Haar systems compatible with groupoid morphisms, An. Univ. Timisoara Ser. Mat.-Inform. 44(2006) no. 2, 19-32. [ISSN 1224-970X].

• D. Covei, Existence results for semilinear elliptic boundary value problems, submitted for publication in Proceedings of Equadiff conference, Viena 2007.

• M. Stoian, Spectral Properties for Locally Bounded Operators, accepted for publication in Proceedings of 21st International Conference on Operator Theory, Timişoara, 2006. (Theta, Bucharest) (eds. R.G. Douglas, J. Esterle, D. Gaspar, D. Timotin and F.-H. Vasilescu).

• D. Covei, Existence of positive solutions to a quasilinear elliptic problem in R^N, Surveys in Mathematics and its Applications, 1 (2006), 111-116. [ISSN 1842-6298].

• N. Chiriac, Normal Anti-Invariant Submanifolds of Paraquaternionic Kahler Manifolds, Surveys in Mathematics and its Applications, 1 (2006), 99-110. [ISSN 1842-6298].

• M. Buneci, Groupoid C*-algebras, Surveys in Mathematics and its Applications, 1 (2006), 71-98. [ISSN 1842-6298].

• M. Stoian, A Functional Calculus for Quotient Bounded Operators, Surveys in Mathematics and its Applications, 1 (2006), 61-70. [ISSN 1842-6298].

• M. Buneci, Borel morphisms and C*-algebras, accepted for publication in Proceedings of 21st International Conference on Operator Theory, Timişoara, 2006. (Theta, Bucharest) (eds. R.G. Douglas, J. Esterle, D. Gaspar, D. Timotin and F.-H. Vasilescu).

• D. Covei, Remark to a quasilinear problem in R^N, Proceedings of MENP-4 (4th International Colloquium Mathematics in Engineering and Numerical Physics), Bucureşti, October 2006.

• I. Chiriac and N. Chiriac, Studiul mărimilor fizice cuadritensoriale în mecanica relativistă, Sesiunea de comunicări ştiinţifice, Globalizare şi identitate", Universitatea Constantin Brâncuşi dinTârgu-Jiu, 2 -3 iunie 2006, vol. I, 499-502.

• I. Chiriac and N. Chiriac, Studiul legilor de conservare ale mărimilor relativiste, Sesiunea de comunicări ştiinţifice, Globalizare şi identitate", Universitatea Constantin Brâncuşi dinTârgu-Jiu, 2 -3 iunie 2006, vol. I, 499-502.

• M. Buneci, Groupoid categories, accepted for publication in Proceedings of Operator Algebras and Mathematical Physics Conference, Bucureşti, 2005. (Theta, Bucharest) (eds. F. Boca, R. Purice, S. Strătilă).

• M. Buneci , Grupoizii în geometria necomutativă, Sesiunea de comunicări ştiinţifice, Globalizare şi identitate", Universitatea Constantin Brâncuşi dinTârgu-Jiu, 2 -3 iunie 2006, vol. I, 499-502.

• D. Covei, Existence of positive solutions to a semilinear problems, Proceedings of International Conference Several aspects of biology, chemistry, informatics, mathematics and physiscs, Oradea, 2005, Analele Universităţii din Oradea, Fascicola Matematică, Tom XIII, 2006, 125-132. [ISSN 1221-1265].

• M. Buneci and P. Stachura, Morphisms of locally compact groupoids endowed with Haar systems , arXiv : math.OA/0511613.

• D. Covei, A few results about the p-Laplace's operator, Acta Univ. Apulensis Math. Inform No. 10 (2005) - Proceedings of the International Conference on Theory and Applications of Mathematics and Informatics (ICTAMI 2005), 105-115. [ISSN 1582-5329]

• D. Covei, Existence and uniqueness of positive solutions to a quasilinear elliptic problem in R^N, Electronic Journal of Differential Equations, No 139, vol.2005(2005), 15 pp. [ISSN 1072-6691].

• M. Stoian, Spectral sets for universally bounded operators, arXiv: math.FA/0511671.