AIS Lie Algebras (2018)

 Speakers with their affiliations:

Sl. No.	Speaker	Affiliation
1	Sachin Sharma	IIT Kanpur
2	PunitaBatra	HRI, Allahabad
3	B. Ravinder	CMI, Chennai
4	TanushreeKhandai	IISER Mohali
5	R. Venkatesh	IISc, Bangalore
6	S.E. Rao	Retired from TIFR, Mumbai

 Names of the tutors and their affiliation

Sl. No.	Tutors	Affiliation
1	Souvik Pal	HRI, Allahabad
2	K.TejaGv	IISc, Bangalore
3	R. Venkatesh	IISc, Bangalore
4	S.E. Rao	Retired from TIFR, Mumbai

 Syllabus:

Sl. No.	Speaker	Actual syllabus covered by each speaker
1	Sachin Sharma	Linear Lie algebras, lie algebras of derivations, Ideals, homomorphism, Representations of lie algebras, Solvable and Nilpotent Lie algebras, Engel’s Theorem, Lie’s Theorem, Jordan chevalley decomposition.
2	PunitaBatra	Cartan’s Criterion – Killing Form, Criterion for semi-simplicity, Inner derivations, Abstract Jordan decomposition, Modules, Casimir element, Weyl’s Theorem, Preservation of Jordan decomposition, Representations of sl (2,F).
3	B. Ravinder	Maximal toralsubalgebras and roots, Orthogonality, Integrality and Rationality Properties of Roots, Root systems, Bases, Weyl chambers, The Weyl group, Irreducible Root Systems, Cartan Matrix.
4	TanushreeKhandai	Universal enveloping algebra,Coxeter graph, Dynkin diagrams, Classification Theorem, Construction of root systems and automorphisms, The theory of weights, Dominant weights, Isomorphism Theorem, CartanSubalgebras.
5	R. Venkatesh	Poincare-Birkhoff-Witt Theorem, Serre’s Theorem, Weights and maximal vectors, Verma modules, Finite dimensional irreducible modules, The finite dimensionality criterion, Multiplicity formula, characters of Verma modules, Weyl’s Character Formula.
6	S.E. Rao	Generalised Cartan matrices and Kac-Moody algebras, Affine Kac-Moody Lie algebras, Toroidal Lie algebras and representation theory.

 Time Table

List of actual participants

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