Special Mathematics Lecture
Contact:
Serge Richard (richard@math.nagoyau.ac.jp), Rm. 237 in Sci. Bldg. A
Groups and their representations (Spring 2018)
Registration code : 0053621
Schedule : Wednesday (18:30  20.00) in room 207 of the Science Building A
Registration: See page 15 of this document

Class dates :
April 11, 18, 25
May 2, 9, 16, 23, 30
June 6, 13, 20, 27
July 4, 11, 18

Program and notes taken by L. Zhang :
1) Groups
Summary on matrices,
lect. 1,
lect. 2,
lect. 3
2) Linear representations
Summary on Hilbert spaces,
lect. 3.5,
lect. 4,
lect. 5,
lect. 6,
lect. 7,
lect. 8
3) Lie groups
lect. 8.5,
lect. 9,
lect. 10
4) Semisimple theory
lect. 11,
lect. 12,
lect. 13,
lect. 14,
lect. 15

At the end of the last lecture :

For the evaluation, you need to submit the solutions of some exercises and/or the proofs of some statements.
These submissions can take place at any time during the semester.
If you have any question, contact me
or Hideki Inoue

Works submitted by the students :
About normal subgroups and quotient groups, by Naohiro Tsuzu
About subgroups, cosets, and homomorphims, by Keito Masuda
Many proofs related to the 1st lecture, by Liyang Zhang
On inner and outer semidirect product, by Song Ha Nguyen and Dang Cong Bui
On Aut(G), by Takuya Ishibashi
About normal subgroups and homomorphisms, by Chang Sun
On tensor product of Hilbert spaces, by Naohiro Tsuzu
Transformation groups and finite subgroups of O(2) , by Liyang Zhang
On nilpotent and solvable Lie algebras, by Takuya Ishibashi
On generalized eigenvectors, by Shihab Fadda
On su(n) and the Killing form, by Son Nguyen, Cong Bui, Song Ha
About the complexification of a Lie algebra, by Sparsh Mishra
On the Killing form, by Zhang Nuozhou
On the Poincare group, by Adrien Levacic
Universal enveloping algebras and Casimir operators, by Yoshihiko Terasawa
On root system, by Cong Bui, Song Ha

References : (electronic version available upon request)
Lecture notes: Theorie des groupes pour la physique, written by W. Amrein.
Excellent, but in French
Book: Group theory in physics, an introduction, written by J.F. Cornwell.
Looks appropriate. Based on previous volumes I and II
Book: Functional analysis I, written M. Reed and B. Simon.
A classical book of functional analysis
Book: A course in the theory of groups, written by D.J. Robinson.
More complicated and more complete, notations not so friendly
Book: Representations of finite and compact groups, written by B. Simon.
Excellent, but little bit advanced
Book: Group theory and physics, written by S. Sternberg.
Looks quite accessible
Book: Lie groups, Lie algebras, and representations: an elementary introduction, written by B. Hall.
Almost everything on linear Lie groups and algebras, quite accessible
Book: Lie algebras in particle physics, from isospin to unified theories, written by H. Georgi.
Written for physicists, but provides a good introduction with many heuristic explanations
Lectures notes: Group theory (for physicists), written by
C. Ludeling.
Covers the main topics
Lecture Notes: Group Theory Summary, written by M. Schaller.
Very brief text
Lecture notes: Group theory
and its applications in physics, written by B. Gutkin.
Much more physically oriented
Lecture notes: Symmetries and groups, written by H. Osborn.
More advanced, with material on gauge groups and gauge theories
Lecture notes: Invariances in Physics
and Group Theory, written by J.B. Zuber.
More advanced, with material on gauge theories
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