First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
MATHEMATICS
Course unit
REPRESENTATION THEORY OF GROUPS
SC01120635, A.A. 2017/18

Information concerning the students who enrolled in A.Y. 2017/18

Information on the course unit
Degree course Second cycle degree in
MATHEMATICS
SC1172, Degree course structure A.Y. 2011/12, A.Y. 2017/18
N0
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Degree course track GENERALE [010PD]
Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination REPRESENTATION THEORY OF GROUPS
Website of the academic structure http://matematica.scienze.unipd.it/2017/laurea_magistrale
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction English
Branch PADOVA
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Lecturers
Teacher in charge GIOVANNA CARNOVALE MAT/02

Mutuated
Course unit code Course unit name Teacher in charge Degree course code
SC01120635 REPRESENTATION THEORY OF GROUPS GIOVANNA CARNOVALE SC1172

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Core courses MAT/02 Algebra 6.0

Mode of delivery (when and how)
Period Second semester
Year 1st Year
Teaching method frontal

Organisation of didactics
Type of hours Credits Hours of
teaching
Hours of
Individual study
Shifts
Practice 2.0 16 34.0 No turn
Lecture 4.0 32 68.0 No turn

Calendar
Start of activities 26/02/2018
End of activities 01/06/2018

Syllabus
Prerequisites: Basic notions in linear algebra and group theory.
Target skills and knowledge: The student will learn the basic notions on complex representations of finite groups and the classification of complex semisimple Lie algebras.
Examination methods: Written, involving a series of exercises.
Assessment criteria: Exams will be evaluated on basis of their completeness, correctness and exactness.
Course unit contents: Representations. Irreducible representations. Maschke's theorem. Orthogonality of characters. Induced representations. Frobenius reciprocity. Rappresentazioni Indotte, formual di Mackey. Reciprocita' di Frobenius. Frobenius-Scur Indicator. Compact groups. Linear algebraic groups and their Lie algebras. Solvable, nilpotent and semisimple Lie algebras. Cartan's criterion. Killing form. Weyl's theorem. Root space decomposition. Root systems. Classification of semisimple Lie algebras. Universal enveloping algebras. Finite dimensional irreducible representations of a semisimple Lie algebra.
Planned learning activities and teaching methods: Classroom lectures.
Additional notes about suggested reading: We will also use a few pages from these Lecture Notes by Alexander Kleschchev
http://darkwing.uoregon.edu/~klesh/teaching/AGLN.pdf
Textbooks (and optional supplementary readings)
  • Serre, Jean-Pierre, Linear representations of finite groupsJean-Pierre Serretranslated from the french by Leonard L. Scott. New York [etc.]: Springer, --. Cerca nel catalogo
  • Humphreys, James E., Introduction to Lie algebras and representation theoryJames E. Humphreys. New York [etc.]: Springer-Verlag, --. Cerca nel catalogo
  • Etingof, Pavel I.; Gerovitch, Slava, Introduction to representation theoryPavel Etingof ... [et al.]with historical interludes by Slava Gerovitch. Providence: American Mathematical Society, 2011. Cerca nel catalogo