Matches in SemOpenAlex for { <https://semopenalex.org/work/W2581330404> ?p ?o ?g. }
Showing items 1 to 64 of
64
with 100 items per page.
- W2581330404 abstract "Following the seminal work of Zhuang, connected Hopf algebras of finite GK-dimension over algebraically closed fields of characteristic zero have been the subject of several recent papers. This thesis is concerned with continuing this line of research and promoting connected Hopf algebras as a natural, intricate and interesting class of algebras. We begin by discussing the theory of connected Hopf algebras which are either commutative or cocommutative, and then proceed to review the modern theory of arbitrary connected Hopf algebras of finite GK-dimension initiated by Zhuang. We next focus on the (left) coideal subalgebras of connected Hopf algebras of finite GK-dimension. They are shown to be deformations of commutative polynomial algebras. A number of homological properties follow immediately from this fact. Further properties are described, examples are considered and invariants are constructed. A connected Hopf algebra is said to be primitively thick if the difference between its GK-dimension and the vector-space dimension of its primitive space is precisely one . Building on the results of Wang, Zhang and Zhuang,, we describe a method of constructing such a Hopf algebra, and as a result obtain a host of new examples of such objects. Moreover, we prove that such a Hopf algebra can never be isomorphic to the enveloping algebra of a semisimple Lie algebra, nor can a semisimple Lie algebra appear as its primitive space. It has been asked in the literature whether connected Hopf algebras of finite GK-dimension are always isomorphic as algebras to enveloping algebras of Lie algebras. We provide a negative answer to this question by constructing a counterexample of GK-dimension 5. Substantial progress was made in determining the order of the antipode of a finite dimensional pointed Hopf algebra by Taft and Wilson in the 1970s. Our final main result is to show that the proof of their result can be generalised to give an analogous result for arbitrary pointed Hopf algebras." @default.
- W2581330404 created "2017-02-03" @default.
- W2581330404 creator A5089491332 @default.
- W2581330404 date "2016-01-01" @default.
- W2581330404 modified "2023-09-23" @default.
- W2581330404 title "Connected Hopf algebras of finite Gelfand-Kirillov dimension" @default.
- W2581330404 hasPublicationYear "2016" @default.
- W2581330404 type Work @default.
- W2581330404 sameAs 2581330404 @default.
- W2581330404 citedByCount "1" @default.
- W2581330404 countsByYear W25813304042017 @default.
- W2581330404 crossrefType "dissertation" @default.
- W2581330404 hasAuthorship W2581330404A5089491332 @default.
- W2581330404 hasConcept C130856480 @default.
- W2581330404 hasConcept C13336665 @default.
- W2581330404 hasConcept C136119220 @default.
- W2581330404 hasConcept C138354692 @default.
- W2581330404 hasConcept C14394260 @default.
- W2581330404 hasConcept C148647251 @default.
- W2581330404 hasConcept C155058155 @default.
- W2581330404 hasConcept C202444582 @default.
- W2581330404 hasConcept C29712632 @default.
- W2581330404 hasConcept C33676613 @default.
- W2581330404 hasConcept C33923547 @default.
- W2581330404 hasConcept C55192134 @default.
- W2581330404 hasConceptScore W2581330404C130856480 @default.
- W2581330404 hasConceptScore W2581330404C13336665 @default.
- W2581330404 hasConceptScore W2581330404C136119220 @default.
- W2581330404 hasConceptScore W2581330404C138354692 @default.
- W2581330404 hasConceptScore W2581330404C14394260 @default.
- W2581330404 hasConceptScore W2581330404C148647251 @default.
- W2581330404 hasConceptScore W2581330404C155058155 @default.
- W2581330404 hasConceptScore W2581330404C202444582 @default.
- W2581330404 hasConceptScore W2581330404C29712632 @default.
- W2581330404 hasConceptScore W2581330404C33676613 @default.
- W2581330404 hasConceptScore W2581330404C33923547 @default.
- W2581330404 hasConceptScore W2581330404C55192134 @default.
- W2581330404 hasLocation W25813304041 @default.
- W2581330404 hasOpenAccess W2581330404 @default.
- W2581330404 hasPrimaryLocation W25813304041 @default.
- W2581330404 hasRelatedWork W127227201 @default.
- W2581330404 hasRelatedWork W1499263904 @default.
- W2581330404 hasRelatedWork W1964654614 @default.
- W2581330404 hasRelatedWork W2049160125 @default.
- W2581330404 hasRelatedWork W2053158936 @default.
- W2581330404 hasRelatedWork W2496900673 @default.
- W2581330404 hasRelatedWork W2697152373 @default.
- W2581330404 hasRelatedWork W2798826438 @default.
- W2581330404 hasRelatedWork W2945617276 @default.
- W2581330404 hasRelatedWork W2949412894 @default.
- W2581330404 hasRelatedWork W2950183874 @default.
- W2581330404 hasRelatedWork W2950766000 @default.
- W2581330404 hasRelatedWork W2951213448 @default.
- W2581330404 hasRelatedWork W2963053364 @default.
- W2581330404 hasRelatedWork W2963159193 @default.
- W2581330404 hasRelatedWork W2963396355 @default.
- W2581330404 hasRelatedWork W2963846210 @default.
- W2581330404 hasRelatedWork W3016413709 @default.
- W2581330404 hasRelatedWork W2188183923 @default.
- W2581330404 hasRelatedWork W2534364955 @default.
- W2581330404 isParatext "false" @default.
- W2581330404 isRetracted "false" @default.
- W2581330404 magId "2581330404" @default.
- W2581330404 workType "dissertation" @default.