The composition Hall algebra of a weighted projective line

Autor:	Olivier Schiffmann, Igor Burban
Rok vydání:	2013
Předmět:	Filtered algebra Discrete mathematics Projective harmonic conjugate Pure mathematics Hall algebra Applied Mathematics General Mathematics Projective line Projective line over a ring Projective space Projective linear group Quaternionic projective space Mathematics
Zdroj:	Journal für die reine und angewandte Mathematik (Crelles Journal). 2013:75-124
ISSN:	1435-5345 0075-4102
DOI:	10.1515/crelle.2012.023
Popis:	In this article, we deal with properties of the reduced Drinfeld double of the composition subalgebra of the Hall algebra of the category of coherent sheaves on a weighted projective line. This study is motivated by applications in the theory of quantized enveloping algebras of some Lie algebras. We obtain a new realization of the quantized enveloping algebras of affine Lie algebras of simply-laced types as well as some new embeddings between them. Moreover, our approach allows to derive new results on the structure of the quantized enveloping algebras of the toroidal algebras of types D4 (1, 1), E6 (1, 1), E7 (1, 1) and E8 (1, 1). In particular, our method leads to a construction of a modular action and allows to define a PBW-type basis for that classes of algebras.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::eef00b9a25597601783a8eb79deb0736 https://doi.org/10.1515/crelle.2012.023 Zobrazit plný text záznamu