*Group theory

This course is part of the programme
Doctoral study programme Physics

Objectives and competences

To obtain proficiency in the study of symmetries of physical systems, and the use of groups to classify and quantify natural phenomenon.

Prerequisites

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Content

The theory of finite and continuous groups, with particular emphasis on aspects that are relevant for the study of physics: discrete groups, Lie groups and Lie algebras.

Intended learning outcomes

Knowledge and understanding:
To obtain proficiency in the study of symmetries of physical systems, and the use of groups to classify and quantify natural phenomenon.

Readings

  1. Hermann Weyl, Symmetry, Princeton University Press, 1983.
  2. Morton Hammermesh, Group Theory and its Application to Physical Problem, Dover Publications, 1989.
  3. Christoph Ludeling, Group Theory (for Physicists), http://cluster353.ddns.net/group/media/Lie/grouptheorynotes.pdf

Assessment

Seminar work. Oral exam. (70/30)

Lecturer's references

Associate professor of Matematics at the University of Nova Gorica.

  1. CRISTEA, Irina Elena, MAHBOOB, Ahsan, KHAN, Noor Mohammad. A new type of fuzzy quasi-ideals of ordered semigroups. Journal of multiple-valued logic and soft computing, ISSN 1542-3980. [Print ed.], 2020, vol. 34, no. 3/4, str. 283-304. [COBISS.SI-ID 15243779]
  2. KANKARAS, Milica, CRISTEA, Irina Elena. Fuzzy reduced hypergroups. Mathematics, ISSN 2227-7390, 2020, vol. 8, iss. 2, str. 1-12, ilustr. https://www.mdpi.com/2227-7390/8/2/263, doi: 10.3390/math8020263. [COBISS.SI-ID 5566715]
  3. CRISTEA, Irina Elena, KOCIJAN, Juš, NOVAK, Michal. Introduction to dependence relations and their links to algebraic hyperstructures. Mathematics, ISSN 2227-7390, 2019, vol. 7, iss. 10, str. 1-14, ilustr. https://doi.org/10.3390/math7100885, doi: 10.3390/math7100885. [COBISS.SI-ID 5453307]
  4. HEIDARI, Dariush, CRISTEA, Irina Elena. Breakable semihypergroups. Symmetry, ISSN 2073-8994, 2019, vol. 11, iss. 1, str. 1-10, ilustr. https://www.mdpi.com/2073-8994/11/1/100, doi: 10.3390/sym11010100. [COBISS.SI-ID 5313787]
  5. JANČIĆ-RAŠOVIĆ, Sanja, CRISTEA, Irina Elena. Hypernear-rings with a defect of distributivity. Filomat, ISSN 0354-5180, 2018, vol. 32, no. 4, str. 1133-1149. http://www.pmf.ni.ac.rs/filomat-content/2018/32-4/32-4-1-6235.pdf, doi: 10.2298/FIL1804133J. [COBISS.SI-ID 5175803]