01228nam--2200397---450-99000587179020331620130715141908.0978-0-415-35530-8(Rilegato)0-415-35530-3(Rilegato)978-0-415-35531-5(Brossura)0-415-35531-1(Brossura)000587179USA01000587179(ALEPH)000587179USA0100058717920130715d2006----km-y0itay50------baengGB||||||||001yyUN Security Councilpractice and promiseEdward C. LuckLondon and New YorkRoutledge2006XIX, 186 p.23 cmGlobal institutionsPubblicato anche in internet (eISBN 978-0-203-9633-5)2001Global institutionsNazioni UniteConsiglio di sicurezzaBNCF341.2323LUCK,Edward C.501240ITsalbcISBD990005871790203316XXIII.1.M. 57577451 G.XXIII.1.M.00293711BKGIUIANNONE9020130715USA011419UN Security Council1085938UNISA06437nam 22006013 450 991096633630332120231110232625.097814704663671470466368(CKB)4940000000609983(MiAaPQ)EBC6715033(Au-PeEL)EBL6715033(RPAM)22488292(PPN)258258403(OCoLC)1266906978(EXLCZ)99494000000060998320210901d2021 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierOn Finite GK-Dimensional Nichols Algebras over Abelian Groups1st ed.Providence :American Mathematical Society,2021.©2021.1 online resource (142 pages)Memoirs of the American Mathematical Society ;v.2719781470448301 1470448300 Includes bibliographical references.Cover -- Title page -- List of Tables -- Chapter 1. Introduction -- 1.1. Antecedents -- 1.2. Points and blocks -- 1.3. The main result -- 1.3.1. The class of braided vector spaces -- 1.3.2. Diagonal type -- 1.3.3. Flourished graphs -- 1.3.4. Organization of the paper and scheme of the proof -- 1.3.5. About the proofs -- 1.3.6. The Poseidon Nichols algebras -- 1.4. Applications -- 1.4.1. Examples of Hopf algebras -- 1.4.2. Domains -- 1.4.3. Co-Frobenius Hopf algebras -- Chapter 2. Preliminaries -- 2.1. Conventions -- 2.2. Nichols algebras of diagonal type -- 2.3. On the Gelfand-Kirillov dimension -- 2.3.1. Basic facts -- 2.3.2. A criterium for infinite \GK -- Chapter 3. Yetter-Drinfeld modules of dimension 2 -- 3.1. Indecomposable modules and blocks -- 3.2. The Jordan plane -- 3.3. The super Jordan plane -- 3.4. Filtrations of Nichols algebras -- 3.5. Proof of Theorem 3.1.2 -- Chapter 4. Yetter-Drinfeld modules of dimension 3 -- 4.1. The setting -- 4.1.1. A block and a point -- 4.1.2. A pale block and a point -- 4.1.3. Indecomposable of dimension 3 -- 4.1.4. Notations -- 4.1.5. Strong interaction -- 4.2. Weak interaction -- 4.2.1. Preparations -- 4.2.2. Proof of Theorem 4.1.3 -- 4.2.3. Proof of Theorem 4.1.1, weak interaction -- 4.3. The Nichols algebras with finite \GK -- 4.3.1. The Nichols algebra \cB(\lstr(1,\ghost)) -- 4.3.2. The Nichols algebra \cB(\lstr(-1,\ghost)) -- 4.3.3. The Nichols algebra \cB(\lstr₋(1,\ghost)) -- 4.3.4. The Nichols algebra \cB(\lstr₋(-1,\ghost)) -- 4.3.5. The Nichols algebra \cB(\lstr( ,1)) -- 4.4. Mild interaction -- 4.4.1. The Nichols algebra \cB(\cyc₁) -- Chapter 5. One block and several points -- 5.1. The setting -- 5.2. Proof of Theorem 5.1.1 ( =1) -- 5.2.1. Weak interaction and the algebra -- 5.2.2. | |=2 -- 5.2.3. | |&gt -- 2 -- 5.3. The Nichols algebras with finite \GK, _{\diag} connected.5.3.1. The Nichols algebra \cB(\lstr( (1|0)₁ -- )), ∈\G_{ }', ≥3 -- 5.3.2. The Nichols algebra \cB(\lstr( (1|0)₁ -- )), ∉\G_{∞} -- 5.3.3. The Nichols algebra \cB(\lstr( (1|0)₂ -- )) -- 5.3.4. The Nichols algebra \cB(\lstr( (1|0)₃ -- )) -- 5.3.5. The Nichols algebra \cB(\lstr( (2|0)₁ -- )) -- 5.3.6. The Nichols algebra \cB(\lstr( (2|1) -- )) -- 5.3.7. The Nichols algebra \cB(\lstr( ₂,2)) -- 5.3.8. The Nichols algebra \cB(\lstr( _{ -1})) -- 5.4. Proof of Theorem 5.1.2 ( =-1) -- 5.4.1. Connected components of _{\diag} -- 5.4.2. The Nichols algebra \cB(\cyc₂) -- 5.4.3. Several components -- 5.4.4. The Nichols algebras with finite \GK, several connected components in _{\diag} -- Chapter 6. Two blocks -- 6.1. The setting -- 6.2. ₁=1 -- 6.3. ₁= ₂=-1 -- Chapter 7. Several blocks, several points -- 7.1. Notations -- 7.2. Several blocks, one point -- 7.3. The Nichols algebras \pos(\bq,\ghost) -- 7.4. Several blocks, several points -- Chapter 8. Appendix -- 8.1. Nichols algebras over abelian groups -- 8.1.1. The context -- 8.1.2. A pale block and a point -- 8.1.3. The block has =1 -- 8.1.4. The block has =-1 -- 8.1.5. The block has = ∈\G₃' -- 8.2. Admissible flourished diagrams -- Bibliography -- Back Cover."We contribute to the classification of Hopf algebras with finite Gelfand-Kirillov dimension, GKdim for short, through the study of Nichols algebras over abelian groups. We deal first with braided vector spaces over Z with the generator acting as a single Jordan block and show that the corresponding Nichols algebra has finite GKdim if and only if the size of the block is 2 and the eigenvalue is 1; when this is 1, we recover the quantum Jordan plane. We consider next a class of braided vector spaces that are direct sums of blocks and points that contains those of diagonal type. We conjecture that a Nichols algebra of diagonal type has finite GKdim if and only if the corresponding generalized root system is finite. Assuming the validity of this conjecture, we classify all braided vector spaces in the mentioned class whose Nichols algebra has finite GKdim. Consequently we present several new examples of Nichols algebras with finite GKdim, including two not in the class alluded to above. We determine which among these Nichols algebras are domains"--Provided by publisher.Memoirs of the American Mathematical Society Hopf algebrasAssociative rings and algebras -- Hopf algebras, quantum groups and related topics -- Ring-theoretic aspects of quantum groupsmscNonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Quantum groups (quantized enveloping algebras) and related deformationsmscHopf algebras.Associative rings and algebras -- Hopf algebras, quantum groups and related topics -- Ring-theoretic aspects of quantum groups.Nonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Quantum groups (quantized enveloping algebras) and related deformations.512/.5516T2017B37mscAndruskiewitsch Nicolás1714852Angiono Iván1800593Heckenberger István1800594MiAaPQMiAaPQMiAaPQBOOK9910966336303321On Finite GK-Dimensional Nichols Algebras over Abelian Groups4345447UNINA02182nam 22004693 450 991015776760332120230807213135.01-59433-555-9(CKB)3710000001009820(MiAaPQ)EBC6535239(Au-PeEL)EBL6535239(OCoLC)974273084(EXLCZ)99371000000100982020210901d2015 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierGold in Trib 1 Flying, Hiking and Gold Prospecting - Adventure in Wild Present-Day Alaska1st ed.Chicago :Publication Consultants,2015.©2015.1 online resource (121 pages)1-888125-11-X Intro -- Title Page -- Copyright -- Table Of Contents -- Foreword -- Ladue Area Map -- Introduction -- 1 The Plan -- 2 Hatcher Pass -- 3 Practice Air Drop -- 4 Powerline Trail -- 5 Polka Night -- 6 Flight to Gulkana -- 7 Air Drop -- 8 Return to Anchorage -- 9 The Drive -- 10 Up to the Ridge -- 11 Day One on the Trail -- 12 Wet Saturday -- 13 Trib 1 at Last -- 14 Trib 2 -- 15 Glory Hole -- 16 A Day of Panning -- 17 One Mean Wet Hike -- 18 Last Day of Hiking -- 19 Hagen's Winter Trip -- 20 Working Gold Claim -- 21 Day of Relaxation -- 22 Last Few Days -- 23 Back to Civilization.Gold in Trib 1 is an account of a flying, hiking, and gold prospecting adventure in wild, present-day Alaska.It is the story of the exploits of two good friends and their adventures while prospecting for gold.It is a factual account where possible and where not factual, it is the way they would have liked it.Alaska--Description and travelProspectingProspecting--AlaskaAlaska--Description and travel.Prospecting.Prospecting--Alaska.917.98Anderson Douglas169119MiAaPQMiAaPQMiAaPQBOOK9910157767603321Gold in Trib 11895627UNINA