Abstract
These lectures provide a brief introduction to group theory, largely focussing on finite groups. After giving the basic definition of groups, we start with a discussion on abelian groups followed by a discussion on non-abelian groups in the next section. Along the way, we define normal subgroups and conjugacy classes and discuss the commutator subgroup and abelianization. In the final sections, we discuss the examples of the Quaternionic group, as well as two examples of continuous groups- the rotation group, in particular its connection with the group of special unitary matrices in two dimensions as well as the conformal group.
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[1] For the discussion on abelian groups, I have mostly followed the book by M. Nakahara, Geometry, Topology and Physics (Taylor & Francis, Boca Raton, FL, USA, 2003). Chapter-3, section- 3.1
[2] The discussion on SO(3) and the homomorphism with SU(2) is discussed in the classical mechanics textbook by J. V. José and E. J. Saletan, Classical Dynamics: A contemporary approach, (Cambridge U. Press, 1998). chapter-8, section-8.2.1, 8.4.
[3] The discussion on conformal transformations is available in many places. One place is the text book by P. Francesco, P. Mathieu and D. Sénéchal, Conformal Field Theory (Springer, New York, 2012).
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Ezhuthachan, B. (2017). Special Topics: A Short Course on Group Theory. In: Bhattacharjee, S., Mj, M., Bandyopadhyay, A. (eds) Topology and Condensed Matter Physics. Texts and Readings in Physical Sciences, vol 19. Springer, Singapore. https://doi.org/10.1007/978-981-10-6841-6_8
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DOI: https://doi.org/10.1007/978-981-10-6841-6_8
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