Lectures on Quantum Groups by Jens Carsten Jantzen

By Jens Carsten Jantzen

When you consider that its foundation approximately ten years in the past, the idea of quantum teams has turn into probably the most interesting issues of contemporary arithmetic, with a number of functions to numerous occasionally particularly disparate parts, together with low-dimensional topology and mathematical physics. This e-book is without doubt one of the first expositions that's particularly directed to scholars who've no earlier wisdom of the topic. the single prerequisite, as well as common linear algebra, is a few acquaintance with the classical idea of advanced semisimple Lie algebras. beginning with the quantum analog of $\mathfrak{sl}_2$, the writer conscientiously leads the reader via all of the information worthwhile for complete realizing of the topic, relatively emphasizing similarities and adjustments with the classical thought. the ultimate chapters of the ebook describe the Kashiwara-Lusztig conception of so-called crystal (or canonical) bases in representations of advanced semisimple Lie algebras. the alternative of the subjects and the fashion of exposition make Jantzen's ebook a great textbook for a one-semester direction on quantum teams.

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