Lie Groups

Luiz Antonio Barrera San Martin is a Full Professor at the University of Campinas, Brazil. He holds a Master's degree in Mathematics (1982) from the University of Campinas, Brazil, and a PhD in Mathematics (1987) from the University of Warwick, England. His research interests are in Lie Theory, more precisely in semigroups, semisimple groups, Lie groups, homogeneous spaces, and flag manifolds.

“An important feature of the book is the presence of a lot of examples illustrating introduced concepts and proven results. Each chapter … accompanied by a fairly many exercises that enable the reader to check the degree of understanding of the material in each chapter and to learn something new. The student can use this book for self-study of the foundations of the theory of Lie groups.” (V. V. Gorbatsevich, zbMATH 1466.22001, 2021)

• Preface.- Introduction.- Part I: Topological Groups.- Topological Groups.- Haar Measure.- Representations of Compact Groups.- Part II: Lie Groups and Algebras.- Lie Groups and Lie Algebras.- Lie Subgroups.- Homomorphism and Coverings.- Series Expansions.- Part III: Lie Algebras and Simply Connected Groups.- The Affine Group and Semi-direct Products.- Solvable and Nilpotent Groups.- Compact Groups.- Noncompact Semi-simple Groups.- Part IV: Transformation Groups.- Lie Group Actions.- Invariant Geometry.- Appendices.