| Title:
|
Presentation of the singular part of the Brauer monoid (English) |
| Author:
|
Maltcev, Victor |
| Author:
|
Mazorchuk, Volodymyr |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
132 |
| Issue:
|
3 |
| Year:
|
2007 |
| Pages:
|
297-323 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We obtain a presentation for the singular part of the Brauer monoid with respect to an irreducible system of generators consisting of idempotents. As an application of this result we get a new construction of the symmetric group via connected sequences of subsets. Another application describes the lengths of elements in the singular part of the Brauer monoid with respect to the system of generators mentioned above. (English) |
| Keyword:
|
semigroup |
| Keyword:
|
presentation |
| Keyword:
|
symmetric group |
| Keyword:
|
Brauer monoid |
| Keyword:
|
irreducible systems of generators |
| Keyword:
|
idempotents |
| MSC:
|
20B30 |
| MSC:
|
20M05 |
| MSC:
|
20M20 |
| idZBL:
|
Zbl 1163.20035 |
| idMR:
|
MR2355660 |
| DOI:
|
10.21136/MB.2007.134125 |
| . |
| Date available:
|
2009-09-24T22:32:00Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134125 |
| . |
| Reference:
|
[1] A. Aǐzenštat: Defining relations of finite symmetric semigroups.Mat. Sb. N. S. 45 (1958), 261–280. (Russian) MR 0101275 |
| Reference:
|
[2] R. Brauer: On algebras which are connected with the semisimple continuous groups.Ann. of Math. 38 (1937), 857–872. Zbl 0017.39105, MR 1503378, 10.2307/1968843 |
| Reference:
|
[3] A. Clifford, G. Preston: The Algebraic Theory of Semigroups. Vol. I.Mathematical Surveys, No. 7, American Mathematical Society, Providence, R.I., 1961. MR 0132791 |
| Reference:
|
[4] J. East: A presentation of the singular part of the symmetric inverse monoid.Preprint, 2004. Zbl 1099.20029, MR 2229484 |
| Reference:
|
[5] G. Kudryavtseva, V. Mazorchuk: On conjugation in some transformation and Brauer-type semigroups.Publ. Math. Debrecen 70 (2007), 19–43. MR 2288466 |
| Reference:
|
[6] G. Kudryavtseva, V. Mazorchuk: On presentation of Brauer-type monoids.Central Europ. J. Math. 4 (2006), 413–434. MR 2233859, 10.2478/s11533-006-0017-6 |
| Reference:
|
[7] G. Kudryavtseva, V. Maltcev, V. Mazorchuk: ${L}$- and ${R}$-cross-sections in the Brauer semigroup.Semigroup Forum 72 (2006), 223–248. MR 2216091, 10.1007/s00233-005-0511-3 |
| Reference:
|
[8] V. Maltcev: Generating systems, ideals and the chief series of the Brauer semigroup.Proceedins of Kyiv University, Physical and Mathematical Sciences (2004), 59–65. |
| Reference:
|
[9] V. Mazorchuk: On the structure of Brauer semigroup and its partial analogue.Problems in Algebra 13 (1998), 29–45. |
| Reference:
|
[10] V. Mazorchuk: Endomorphisms of $n$, ${P}{B}_n$ and $n$.Comm. Algebra 30 (2002), 3489–3513. MR 1915009 |
| . |
