On minimal quasitriangular pointed Hopf~ algebras

Journal of Mathematical Sciences

Masuoka, Akira¹ 

关键词: Hopf algebra;    Nichols algebra;    generalized quantum double;    quasitriangular;   

DOI  :  

学科分类：数学（综合）

来源: University of Tokyo * Department of Mathematical Sciences

【 摘 要 】

Thequantizedenvelopingalgebra$U_q$isconstructedasaquotientofthegeneralizedquantumdouble$U^{leq0}_qcmdbicross_{au}U^{geq0}_q$associatedtoanaturalskewpairing$au:U^{leq0}_qotimesU^{geq0}_qightarrowk$.Thisdoubleisgeneralizedbyegin{equation*}cmdcalD=(cmdfrakB(V)cmddotrtimesF)cmdbicross_{au}(cmdfrakB(W)cmddotrtimesG),end{equation*}where$F$,$G$areabeliangroups,$Vin{}^F_FcmdcalYD$,$Win{}^G_GcmdcalYD$areYetter-Drinfeldmodulesand$cmdfrakB(V)$,$cmdfrakB(W)$aretheirNicholsalgebras.WeprovesomeresultsonHopfidealsof$cmdcalD$,includingacharacterizationofwhatwecallthinHopfideals.AsanapplicationwegiveanexplicitdescriptionofthoseminimalquasitriangularpointedHopfalgebrasincharacteristiczerowhicharegeneratedbyskewprimitives.

【 授权许可】

Unknown