Inverse Semigroups

by Lawson, Mark V.

• ISBN13: 9789810233167
• ISBN10: 9810233167
• Format: Hardcover
• Copyright: 1999-02-01
• Publisher: WORLD SCIENTIFIC PUB CO INC

Summary

"this volume represents an outstanding contribution to the field. The resolute graduate student or mature researcher, alike, can find a wealth of directions for future work".Mathematical Reviews

Table of Contents

Preface	vii
1 Introduction to inverse semigroups	1	(46)
1.1 The origins of inverse semigroups	1	(9)
1.2 Pseudogroups and local structures	10	(5)
1.3 Symmetry	15	(2)
1.4 Abstract inverse semigroups	17	(19)
1.5 Representation theorems	36	(3)
1.6 Notes on Chapter 1	39	(8)
2 Extending partial symmetries	47	(28)
2.1 Partial symmetries	48	(8)
2.2 E-unitary covers	56	(2)
2.3 Congruences	58	(4)
2.4 The minimum group congruence	62	(7)
2.5 Notes on Chapter 2	69	(6)
3 The natural partial order	75	(32)
3.1 The associated groupoid	76	(6)
3.2 Green's relations	82	(11)
3.3 Primitive inverse semigroups	93	(4)
3.4 The bicyclic monoid	97	(6)
3.5 Notes on Chapter 3	103	(4)
4 Ordered groupoids	107	(26)
4.1 Inductive groupoids	108	(8)
4.2 Ordered groupoids from *-semigroups	116	(8)
4.3 Ordered congruences	124	(6)
4.4 Notes on Chapter 4	130	(3)
5 Extensions of inverse semigroups	133	(38)
5.1 The Kernel-trace description of a congruence	134	(4)
5.2 Idempotent-separating extensions	138	(9)
5.3 Lambda-semidirect products	147	(13)
5.4 Inverse Omega-semigroups	160	(7)
5.5 Notes on Chapter 5	167	(4)
6 Free inverse semigroups	171	(26)
6.1 The existence of free inverse semigroups	171	(3)
6.2 Solving the word problem	174	(11)
6.3 The structure of free inverse semigroups	185	(2)
6.4 Munn normal form	187	(7)
6.5 Notes on Chapter 6	194	(3)
7 E-unitary inverse semigroups	197	(36)
7.1 Division theorems	198	(10)
7.2 The P-theorem	208	(8)
7.3 The Mobius inverse monoid	216	(5)
7.4 F-inverse semigroups	221	(5)
7.5 F-inverse covers	226	(4)
7.6 Notes on Chapter 7	230	(3)
8 Enlargements	233	(40)
8.1 A coordinate-free P-theorem	233	(6)
8.2 E-unitary covers	239	(9)
8.3 The maximum enlargement theorem	248	(11)
8.4 Applications	259	(11)
8.5 Notes on Chapter 8	270	(3)
9 O-E-unitary inverse semigroups	273	(58)
9.1 The structure of a class of O-E-unitary inverse semigroups	274	(4)
9.2 Kellendonk's topological groupoid	278	(7)
9.3 Polycyclic monoids	285	(19)
9.4 McAlister semigroups	304	(14)
9.5 Tiling semigroups	318	(9)
9.6 Notes on Chapter 9	327	(4)
10 Category actions and inverse semigroups	331	(42)
10.1 Inverse semigroups from category actions	332	(3)
10.2 A coordinatisation theorem	335	(6)
10.3 Category actions from inverse semigroups	341	(4)
10.4 Functors between systems and semigroups	345	(2)
10.5 Equivalent systems	347	(6)
10.6 Composing the functors	353	(5)
10.7 Special cases	358	(11)
10.8 Notes on Chapter 10	369	(4)
Bibliography	373	(32)
Index	405