Hopf algebras and root systems

Hopf algebras and root systems /

Saved in:
Bibliographic Details
Main Authors: Heckenberger, István, 1969- (Author), Schneider, Hans-Jürgen, 1944- (Author)
Corporate Author: ProQuest (Firm)
Format: Electronic eBook
Language:English
Published: Providence, Rhode Island : American Mathematical Society, [2020]
Series:Mathematical surveys and monographs ; no. 247.
Subjects:
Hopf algebras.
Root systems (Algebra)
Weyl groups.
Online Access:Connect to this title online (unlimited simultaneous users allowed; 325 uses per year)

MARC

LEADER 00000nam a2200000 i 4500
001 b3823977
003 CStclU
005 20210509145102.3
006 m d
007 cr cnu---unuuu
008 200516t20202020riua ob 000 0 eng d
020 |a 147045680X  |q (electronic bk.) 
020 |a 9781470456801  |q (electronic bk.) 
020 |z 9781470452322  |q (hardcover) 
020 |z 1470452324  |q (hardcover) 
035 |a (NhCcYBP)ebc6195967 
040 |a NhCcYBP  |c NhCcYBP 
050 4 |a QA613.8  |b .H43 2020 
082 0 4 |a 512/.55  |2 23 
100 1 |a Heckenberger, István,  |d 1969-  |e author. 
245 1 0 |a Hopf algebras and root systems /  |c István Heckenberger, Hans-Jürgen Schneider. 
264 1 |a Providence, Rhode Island :  |b American Mathematical Society,  |c [2020] 
264 4 |c ©2020 
300 |a 1 online resource ( xix, 582 pages) :  |b illustrations 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
490 1 |a Mathematical surveys and monographs ;  |v volume 247 
504 |a Includes bibliographical references (pages 565-574) and indexes. 
505 0 0 |a Machine generated contents note:   |g pt. 1   |t Hopf algebras, Nichols algebras, braided monoidal categories, and quantized enveloping algebras --   |g ch. 1   |t Quick Introduction To Nichols Algebras --   |g 1.1.  |t Algebras, coalgebras, modules and comodules --   |g 1.2.  |t Bialgebras and Hopf algebras --   |g 1.3.  |t Strictly graded coalgebras --   |g 1.4.  |t Yetter-Drinfeld modules over a group algebra --   |g 1.5.  |t Braided vector spaces of group type --   |g 1.6.  |t Braided Hopf algebras and Nichols algebras over groups --   |g 1.7.  |t Braid group and braided vector spaces --   |g 1.8.  |t Shuffle permutations and braided shuffle elements --   |g 1.9.  |t Braided symmetrizer and Nichols algebras --   |g 1.10.  |t Examples of Nichols algebras --   |g 1.11.  |t Notes --   |g ch. 2   |t Basic Hopf Algebra Theory --   |g 2.1.  |t Finiteness properties of coalgebras and comodules --   |g 2.2.  |t Duality --   |g 2.3.  |t restricted dual --   |g 2.4.  |t Basic Hopf algebra examples --   |g 2.5.  |t Coinvariant elements --   |g 2.6.  |t Actions and coactions --   |g 2.7.  |t Cleft objects and two-cocycles --   |g 2.8.  |t Two-cocycle deformations and Drinfeld double --   |g 2.9.  |t Notes --   |g ch. 3   |t Braided Monoidal Categories --   |g 3.1.  |t Monoidal categories --   |g 3.2.  |t Braided monoidal categories and graphical calculus --   |g 3.3.  |t Modules and comodules over braided Hopf algebras --   |g 3.4.  |t Yetter-Drinfeld modules --   |g 3.5.  |t Duality and Hopf modules --   |g 3.6.  |t Smash products and smash coproducts --   |g 3.7.  |t Adjoint action and adjoint coaction --   |g 3.8.  |t Bosonization --   |g 3.9.  |t Characterization of smash products and coproducts --   |g 3.10.  |t Hopf algebra triples --   |g 3.11.  |t Notes --   |g ch. 4   |t Yetter-Drinfeld Modules Over Hopf Algebras --   |g 4.1.  |t braided monoidal category of Yetter-Drinfeld modules --   |g 4.2.  |t Duality of Yetter-Drinfeld modules --   |g 4.3.  |t Hopf algebra triples and bosonization --   |g 4.4.  |t Finite-dimensional Yetter-Drinfeld Hopf algebras are Frobenius algebras --   |g 4.5.  |t Induction and restriction functors for Yetter-Drinfeld modules --   |g 4.6.  |t Notes --   |g ch. 5   |t Gradings And Nitrations --   |g 5.1.  |t Gradings --   |g 5.2.  |t Filtrations and gradings by totally ordered abelian monoids --   |g 5.3.  |t coradical filtration --   |g 5.4.  |t Pointed coalgebras --   |g 5.5.  |t Graded Yetter-Drinfeld modules --   |g 5.6.  |t Notes --   |g ch. 6   |t Braided Structures --   |g 6.1.  |t Braided vector spaces --   |g 6.2.  |t Braided algebras, coalgebras and bialgebras --   |g 6.3.  |t fundamental theorem for pointed braided Hopf algebras --   |g 6.4.  |t braided tensor algebra --   |g 6.5.  |t Notes --   |g ch. 7   |t Nichols Algebras --   |g 7.1.  |t Nichols algebra of a braided vector space and of a Yetter-Drinfeld module --   |g 7.2.  |t Duality of Nichols algebras --   |g 7.3.  |t Differential operators for Nichols algebras --   |g 7.4.  |t Notes --   |g ch. 8   |t Quantized Enveloping Algebras And Generalizations --   |g 8.1.  |t Construction of the Hopf algebra Uq --   |g 8.2.  |t YD-data and linking --   |g 8.3.  |t Hopf algebra U(, λ) --   |g 8.4.  |t Perfect linkings and multiparameter quantum groups --   |g 8.5.  |t Notes --   |g pt. 2   |t Cartan graphs, Weyl groupoids, and root systems --   |g ch. 9   |t Cartan Graphs And Weyl Groupoids --   |g 9.1.  |t Axioms and examples --   |g 9.2.  |t Reduced sequences and positivity of roots --   |g 9.3.  |t Weak exchange condition and longest elements --   |g 9.4.  |t Coxeter groupoids --   |g 9.5.  |t Notes --   |g ch. 10   |t Flu-Structure Of Cartan Graphs And Root Systems --   |g 10.1.  |t Coverings and decompositions of Cartan graphs --   |g 10.2.  |t Types of Curtail matrices --   |g 10.3.  |t Classification of finite Cartan graphs of rank two --   |g 10.4.  |t Root systems --   |g 10.5.  |t Notes --   |g ch. 11   |t Cart An Graphs Of Lie Superalgebras --   |g 11.1.  |t Lie superalgebras --   |g 11.2.  |t Cart an graphs of regular Kac-Moody superalgebras --   |g 11.3.  |t Notes --   |g pt. 3   |t Weyl groupoids and root systems of Nichols algebras --   |g ch. 12   |t Braided Monoidal Isomorphism Of Yetter-Drinfeld Modules --   |g 12.1.  |t Dual pairs of Yetter-Drinfeld Hopf algebras --   |g 12.2.  |t Rational modules --   |g 12.3.  |t braided monoidal isomorphism (Ω, ω) --   |g 12.4.  |t One-sided coideal subalgebras of braided Hopf algebras --   |g 12.5.  |t Notes --   |g ch. 13   |t Nichols Systems, And Semi-Cartan Graph Of Nichols Algebras --   |g 13.1.  |t Z-graded Yetter-Drinfeld modules --   |g 13.2.  |t Projections of Nichols algebras --   |g 13.3.  |t adjoint action in Nichols algebras --   |g 13.4.  |t Reflections of Yetter-Drinfeld modules --   |g 13.5.  |t Nichols systems and their reflections --   |g 13.6.  |t semi-Cartan graph of a Nichols algebra --   |g 13.7.  |t Notes --   |g ch. 14   |t Right Coideal Subalgebras Of Nichols Systems, And Cartan Graph Of Nichols Algebras --   |g 14.1.  |t Right coideal subalgebras of Nichols systems --   |g 14.2.  |t Exact factorizations of Nichols systems --   |g 14.3.  |t Hilbert series of right coideal subalgebras of Nichols algebras --   |g 14.4.  |t Tensor decomposable Nichols algebras --   |g 14.5.  |t Nichols algebras with finite Cartan graph --   |g 14.6.  |t Tensor decomposable right coideal subalgebras --   |g 14.7.  |t Notes --   |g pt. 4   |t Applications --   |g ch. 15   |t Nichols Algebras Of Diagonal Type --   |g 15.1.  |t Reflections of Nichols algebras of diagonal type --   |g 15.2.  |t Root vector sequences --   |g 15.3.  |t Rank two Nichols algebras of diagonal type --   |g 15.4.  |t Application to Nichols algebras of rank three --   |g 15.5.  |t Primitively generated braided Hopf algebras --   |g 15.6.  |t Notes --   |g ch. 16   |t Nichols Algebras Of Cartan Type --   |g 16.1.  |t Yetter-Drinfeld modules over a Hopf algebra of polynomials --   |g 16.2.  |t On the structure of U+q --   |g 16.3.  |t On the structure of u+q --   |g 16.4.  |t characterization of Nichols algebras of finite Cartan type --   |g 16.5.  |t Application to the Hopf algebras U(, λ) --   |g 16.6.  |t Notes --   |g ch. 17   |t Nichols Algebras Over Non-Abelian Groups --   |g 17.1.  |t Finiteness criteria for Nichols algebras over non-abelian groups --   |g 17.2.  |t Finite-dimensional Nichols algebras of simple Yetter-Drinfeld modules --   |g 17.3.  |t Nichols algebras with finite root system of rank two --   |g 17.4.  |t Outlook --   |g 17.5.  |t Notes. 
533 |a Electronic reproduction.  |b Ann Arbor, MI  |n Available via World Wide Web. 
588 0 |a Print version record. 
650 0 |a Hopf algebras. 
650 0 |a Root systems (Algebra) 
650 0 |a Weyl groups. 
700 1 |a Schneider, Hans-Jürgen,  |d 1944-  |e author. 
710 2 |a ProQuest (Firm) 
776 0 8 |i Print version:  |a Heckenberger, István, 1969-  |t Hopf algebras and root systems.  |d Providence, Rhode Island : American Mathematical Society, [2020]  |z 9781470452322  |w (DLC) 2019059299 
830 0 |a Mathematical surveys and monographs ;  |v no. 247. 
856 4 0 |u https://ebookcentral.proquest.com/lib/santaclara/detail.action?docID=6195967  |z Connect to this title online (unlimited simultaneous users allowed; 325 uses per year)  |t 0 
907 |a .b38239772  |b 211018  |c 211018 
998 |a uww  |b    |c m  |d z   |e l  |f eng  |g riu  |h 0 
917 |a GOBI ProQuest DDA 
919 |a .ulebk  |b 2020-07-09 
999 f f |i a95f5037-a520-5748-afda-055ffc499a90  |s 1fa69297-d685-54de-a241-c782741369eb  |t 0 

Similar Items