Arrow graph representation showing a cluster with Quantum Group View Homepage


Ontology type: schema:MonetaryGrant     


Grant Info

YEARS

2007-2009

FUNDING AMOUNT

250000 CNY

ABSTRACT

We study a relation between the generic extension graph of representations of a Dynkin quiver and the global crystal graph of its corresponding quantum enveloping algebra. We determine the generators and relations of the generic extension monoid of nilpotent representations of a cyclic quiver. We prove that Ringel-Hall algebras satisfy the fundamental relations in a more general setting and relate the Ringel-Hall algebra of an algebra with those of its quotient algebras. We present applications of Frobenius morphsim theory in the derived categories and stable module categories of repetitive categories of algebras, as well as to study the relationship among monomial, PBW and canonical bases for a non-simply laced quantum enveloping algebra of finite type. We give a criterion for a monomial in an arbitrary quantum enveloping algebra to be tight. We use the Hall algebras of cyclic quivers to study affine quantum Schur-Weyl theory. Using the deformed preprojective algebras, we study irreducible representations of a restricted quantum group. We describe the crystal graphs of representations of a class of quantum superalgebras in terms of Young tableaux. We also study the entwining structure of monods and comonods, and classify infinite dimensional pointed Hopf algebras of GK-dimnesion two and three. Write jointly a b More... »

URL

http://npd.nsfc.gov.cn/projectDetail.action?pid=10671016

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