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Hopf Actions of Bosonizations on Pat...

Del Real Ramos, Kevin,

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Hopf Actions of Bosonizations on Path Algebras of Quivers /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Hopf Actions of Bosonizations on Path Algebras of Quivers // Kevin Del Real Ramos.
作者:	Del Real Ramos, Kevin,
面頁冊數:	1 electronic resource (59 pages)
附註:	Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
Contained By:	Dissertations Abstracts International86-12B.
標題:	Mathematics. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31998773
ISBN:	9798286434749

Hopf Actions of Bosonizations on Path Algebras of Quivers /
Del Real Ramos, Kevin,

Hopf Actions of Bosonizations on Path Algebras of Quivers /Kevin Del Real Ramos. - 1 electronic resource (59 pages)

Source: Dissertations Abstracts International, Volume: 86-12, Section: B.

In this dissertation we continue work of Kinser and Oswald [KO21] which classified Hopf actions of several families of Hopf algebras related to Uq(sl2) on path algebras of quivers, restricting attention to actions which preserve the ascending filtration of the path algebra by path length. In particular, we use their results on actions of Taft algebras to study actions of Bosonizations of quantum linear space with the group algebras, denoted B := R(g1, ..., gθ, χ1, ..., χθ)#kG. For these Bosonizations, we follow the exposition of Cline and Gaddis [CG20]. We are able to utilize the work of Kinser and Oswald as a starting point for this investigation because these Bosonizations that we study are generated by Taft subalgebras. We carefully analyze the necessary conditions for actions of the Taft subalgebras on path algebras to be compatible, and thus glue to an action of the full Bosonization. Then, under certain nontriviality assumptions about the action, we are able to classify Hopf actions of B on path algebras of a quiver.

English

ISBN: 9798286434749Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Bosonizations

Hopf Actions of Bosonizations on Path Algebras of Quivers /
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502 $b Ph.D. $c The University of Iowa $d 2025.
520 $a In this dissertation we continue work of Kinser and Oswald [KO21] which classified Hopf actions of several families of Hopf algebras related to Uq(sl2) on path algebras of quivers, restricting attention to actions which preserve the ascending filtration of the path algebra by path length. In particular, we use their results on actions of Taft algebras to study actions of Bosonizations of quantum linear space with the group algebras, denoted B := R(g1, ..., gθ, χ1, ..., χθ)#kG. For these Bosonizations, we follow the exposition of Cline and Gaddis [CG20]. We are able to utilize the work of Kinser and Oswald as a starting point for this investigation because these Bosonizations that we study are generated by Taft subalgebras. We carefully analyze the necessary conditions for actions of the Taft subalgebras on path algebras to be compatible, and thus glue to an action of the full Bosonization. Then, under certain nontriviality assumptions about the action, we are able to classify Hopf actions of B on path algebras of a quiver.
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590 $a School code: 0096
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
650 4 $a Applied mathematics. $3 2122814
650 4 $a Theoretical physics. $3 2144760
653 $a Bosonizations
653 $a Hopf actions
653 $a Hopf algebras
653 $a Quantum linear space
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790 $a 0096
791 $a Ph.D.
792 $a 2025
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31998773