This volume is a compilation of lectures on algebras and combinatorics presented at the Second International Congress in Algebra and Combinatorics. It reports on not only new results, but also on open problems in the field. The proceedings volume is useful for graduate students and researchers in algebras and combinatorics. The contributors include eminent figures such as E Bannai, P Hilton, M Jambu, I Kotsireas, B Schein and A Smoktunowicz.
Author(s): K. P. Shum, E. Zelmanov, Jiping Zhang, Li Shangzhi
Publisher: World Scientific Publishing Company
Year: 2008
Language: English
Pages: 384
Tags: Математика;Общая алгебра;
Contents......Page 10
Preface......Page 6
1. Introduction......Page 12
2. (x(Yz)) = ((z(yy))z) graph algebras......Page 14
3. Identities in (x(yz)) = ((z(yy))z) graph algebras......Page 17
4. The (x(yz)) = ((z(yy))z) class......Page 19
5. Hyperidentities in the class (x(yz)) = ((z(yy))r) graph algebras......Page 22
References......Page 28
1. Introduction......Page 30
2. Valuations......Page 31
3. Completions of quantum fields......Page 32
4. Projective module, elementary matrices and Morit a-equivalence......Page 33
5. Automorphisms of generic quantum polynomials......Page 34
6. Commutative subalgebras......Page 37
7. Actions of Hopf algebras......Page 38
8. Actions of pointed finite dimensional Hopf algebras......Page 42
9. Poisson structures......Page 43
References......Page 44
1. Introduction......Page 46
2. CD-lemma for associative algebras......Page 48
3.1. CD-Lemma and HNN-extensions......Page 50
3.2. Dialgebreas......Page 51
3.3. Free I?-algebras k(X;I')......Page 52
3.4. Tensor product of free algebras......Page 53
4.1. Schreier extensions of groups......Page 54
4.2. Extensions of algebras......Page 56
4.3. Anti-commutative algebras......Page 57
4.4. Akivis algebras......Page 58
4.5. Some one-relator groups......Page 59
4.6. The Chinese monoid......Page 60
5.2. Shirshov’s CD-lemma for Lie algebras......Page 61
5.3. CD-lemma for modules......Page 63
References......Page 64
1. Introduction......Page 68
2. Preliminaries......Page 69
3. Simplicities......Page 71
4. Derivations of the algebras WNn,o,,l and WNn,n,Ol......Page 72
References......Page 78
1. Introduction......Page 80
2. Idempotent and Regular Elements......Page 82
3. Bands of n-ary Cooperations......Page 86
4. Green's relations L and R......Page 91
References......Page 93
1. Preliminaries......Page 94
2. Term Operations of Derived Algebras......Page 97
3. Surjective Hypersubstitutions of Type T......Page 99
4. i-closed Varieties......Page 103
References......Page 104
1. Introduction......Page 106
2. Weak*-continuous linear operators......Page 109
3.1. The divided powers Banach coalgebra of the p-adic continuous functions on Z,......Page 113
3.2. The Hopf algebra C(Vq,K) for K of residue characteristic p......Page 116
3.2.1. Substitution in M(V,, K ) .......Page 119
3.2.2. The coalgebra endomorphisms of C(Vq, K ).......Page 125
References......Page 128
1. Introduction......Page 130
2. Preliminaries......Page 131
3. Main results......Page 134
References......Page 138
Stability of the Theory of Existentially Closed S-Acts over a Right Coherent Monoid S J. Fountain and V. Gould......Page 140
1. Introduction......Page 141
2. Preliminaries......Page 144
3. Types......Page 147
4. U-rank and superstability of TS......Page 150
5. Total transcendence of Ts......Page 154
References......Page 164
Paper-Folding, Polygons, Complete Symbols, and the Euler Totient Function: An Ongoing Saga Connecting Geometry, Algebra, and Number Theory P. Hilton, J. Pedersen and B. Walden......Page 168
1. Introduction......Page 169
2. The Generalized Quasi-order Theorem......Page 180
3. The Generalized Coach Theorem......Page 183
4. Some corollaries......Page 187
References......Page 188
1. Koszul Duality and Koszul Algebras (overall)......Page 190
2. Hyperplane Arrangements......Page 192
2.1. Holonomy Lie Algebra......Page 194
2.2. Hypersolvable Arrangements......Page 195
References......Page 198
1. Basic Definitions......Page 200
2. Prime classical and non-classical varieties......Page 203
3. Prime subvarieties of VarMz(F)......Page 207
4. Trace-killers for M3(F)......Page 212
6. Matrix type of some algebras......Page 213
References......Page 214
1. Introduction......Page 216
2. Conformal algebras......Page 217
3. TC-algebras......Page 222
4. Irreducible TC-subalgebras of matrix Weyl algebras......Page 224
References......Page 227
1. Introduction......Page 230
3. Main results......Page 231
References......Page 234
1. Introduction......Page 236
2. Subgroups of PSLa(Z)......Page 237
3.1. Special Polygons......Page 238
3.2. Farey Symbols......Page 241
3.3. Generators......Page 243
3.4. Group Invariants......Page 244
4. Coset Permutation Representation of a Group......Page 245
5.1. Calculating a Farey Symbol......Page 246
5.2. Group Membership......Page 250
5.3. Coset Representatives......Page 251
6. Implementation......Page 252
References......Page 253
1. Introduction......Page 254
2. Grobner-Shirshov bases......Page 255
3. Coxeter groups of types E6 and Er......Page 256
4. Grobner-Shirshov basis of the Coxeter group Eo......Page 257
5. Grobner-Shirshov basis of the Coxeter group E7......Page 260
References......Page 265
2. Notations......Page 268
3. Main Results......Page 270
4. Some Preliminary Results......Page 271
5. Group Extension by an Element with Zero Entries......Page 272
6. Proof of Theorem 3.1......Page 281
References......Page 284
1. Introduction......Page 286
2. A formal language for symbolic calculus......Page 287
3. G-calculus: A logical Inference System......Page 288
4. Necessary antecedents of formal consequences......Page 290
5. R-refutation and R-contraction......Page 292
6. R-calculus......Page 293
7. Reachability, soundness and completeness......Page 299
8. Basic theorem of testing......Page 301
References......Page 302
Some Remarks on the Burnside Problem for Loops P. Plaumann and L. Sabinina......Page 304
References......Page 312
1. Introduction......Page 314
2. rpp Semigroups......Page 316
3. Quasi-adequate semigroups and cyber groups......Page 325
4. Quasi-C-Ehresmann semigroups and their subclasses......Page 332
5. Some applications......Page 338
6. Conclusion......Page 340
References......Page 343
2. Modular Functor......Page 346
3.1. Non-Abelian Conformal Field Theory......Page 349
3.2. Abelian Conformal Field Theory......Page 359
4.2. Construction of Modular Functor......Page 361
References......Page 363
1. Introduction......Page 364
2.1. The co-adjoint Representation and K-orbits......Page 366
3. The Main Result......Page 368
Acknowledgement......Page 380
References......Page 381
