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Lie algebras, spring 2012

Lecturer

Jouko Mickelsson

Scope

10 cu.

Type

Advanced studies

Prerequisites

A good command of Linear algebra and matrices I-II and Algebra I.

Lectures

Weeks 3-9 and 11-18, Monday 10-12 and Tuesday 10-12 in room B322. Two hours of exercise classes per week.

Easter holiday 5.-11.4.

Exams

Written examination on 15th of May, 12-16 ('yleistentti')

Bibliography

Lecture notes, Jouko Mickelsson:

Lie algebras and quantum groups

Related material:

James Humphreys: Introduction to Lie algebras and representation theory. Graduate Texts

in Mathematics 9, Springer Verlag.

W. Fulton and J. Harris: Representation Theory. Graduate Texts in Mathematics 129, Springer Verlag.

Registration

Did you forget to register? What to do.

Exercise groups

Group

Day

Time

Place

Instructor

1.

Wed

10-12

B322

Antti Harju

Homework exercises

Set 1, January 25: Exercises 1.1.5, 1.1.7, 1.1.9, 1.1.10, the first part in 1.1.11 (concerning the 3 dimensional algebras),
and 1.1.12. Use the most recent version of the lecture notes on the net! Please, give the written solutions to Antti
Harju, at latest on Wednesday 10.15!

Set 2, February 1: Exercises 1.2.5, 1.2.6, 1.2.7, 1.3.11, 1.3.12, 1.3.14

Set 3, February 8: Exercises 1.3.15, 2.1.6, 2.1.7, 2.1.8, 2.2.11, 2.2.12, 2.2.13

Set 4, February 15: Exercises 2.3.15, 2.3.16, 2.3.17, 2.3.18, 2.3.22, 2.3.23

Set 5, February 22: Exercises 2.3.24, 2.3.25, 3.2.5, 3.2.6, 3.2.7, 3.2.8, 3.4.8

Set 6, February 29: Exercises 3.4.6, 3.4.7, 3.4.9, 3.4.10, 3.5.12, 3.5.13, 3.5.14

Set 7, March 14: Exercises 3.6.10, 3.6.11, 3.6.12, 3.6.13, 4.1.6, 4.1.7

Set 8, March 21: Exercises 4.3.5, 4.5.4, 4.5.5, 4.5.6, 4.6.8, 4.6.9

Set 9, March 28: Exercises 4.6.10, 4.6.11, 5.2.2, 5.2.3, 5.2.6, 5.2.7

Set 10, April 4: Exercises 5.3.2, 5.4.14, 5.5.12, 5.5.15, 5.5.17

NO exercises or lectures during the week 15 (April 9 - April 11) because of Easter break.
No exercises or lectures during the week 16.

Set 11, April 25: Exercises 5.5.16, 6.1.2, 6.1.3, 6.1.6, 6.1.12

Set 12, May 9: Exercises 6.2.1, 6.2.3, 6.2.4, 6.3.3, 6.4.1, 6.4.4

EXAMINATION 15/5 ! Either room A111 or B123 in Exactum. Check on the door!

EXAMINATION, summer 2012: June 14, in A111 or B123

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