Geodesic
Presentation of the singular part of the Brauer monoid
Mathematica Bohemica, Tome 132 (2007) no. 3, pp. 297-323
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.21136/MB.2007.134125
Classification : 20B30, 20M05, 20M20
Keywords: semigroup; presentation; symmetric group; Brauer monoid; irreducible systems of generators; idempotents 
@article{10_21136_MB_2007_134125,
     author = {Maltcev, Victor and Mazorchuk, Volodymyr},
     title = {Presentation of the singular part of the {Brauer} monoid},
     journal = {Mathematica Bohemica},
     pages = {297--323},
     year = {2007},
     volume = {132},
     number = {3},
     doi = {10.21136/MB.2007.134125},
     mrnumber = {2355660},
     zbl = {1163.20035},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2007.134125/}
}
TY  - JOUR
AU  - Maltcev, Victor
AU  - Mazorchuk, Volodymyr
TI  - Presentation of the singular part of the Brauer monoid
JO  - Mathematica Bohemica
PY  - 2007
SP  - 297
EP  - 323
VL  - 132
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2007.134125/
DO  - 10.21136/MB.2007.134125
LA  - en
ID  - 10_21136_MB_2007_134125
ER  - 
%0 Journal Article
%A Maltcev, Victor
%A Mazorchuk, Volodymyr
%T Presentation of the singular part of the Brauer monoid
%J Mathematica Bohemica
%D 2007
%P 297-323
%V 132
%N 3
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2007.134125/
%R 10.21136/MB.2007.134125
%G en
%F 10_21136_MB_2007_134125
Maltcev, Victor; Mazorchuk, Volodymyr. Presentation of the singular part of the Brauer monoid. Mathematica Bohemica, Tome 132 (2007) no. 3, pp. 297-323. doi: 10.21136/MB.2007.134125

[1] A. Aǐzenštat: Defining relations of finite symmetric semigroups. Mat. Sb. N. S. 45 (1958), 261–280. (Russian) | MR

[2] R. Brauer: On algebras which are connected with the semisimple continuous groups. Ann. of Math. 38 (1937), 857–872. | DOI | MR | Zbl

[3] A. Clifford, G. Preston: The Algebraic Theory of Semigroups. Vol. I. Mathematical Surveys, No. 7, American Mathematical Society, Providence, R.I., 1961. | MR

[4] J. East: A presentation of the singular part of the symmetric inverse monoid. Preprint, 2004. | MR | Zbl

[5] G. Kudryavtseva, V. Mazorchuk: On conjugation in some transformation and Brauer-type semigroups. Publ. Math. Debrecen 70 (2007), 19–43. | MR

[6] G. Kudryavtseva, V. Mazorchuk: On presentation of Brauer-type monoids. Central Europ. J. Math. 4 (2006), 413–434. | DOI | MR

[7] G. Kudryavtseva, V. Maltcev, V. Mazorchuk: ${L}$- and ${R}$-cross-sections in the Brauer semigroup. Semigroup Forum 72 (2006), 223–248. | DOI | MR

[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.

[9] V. Mazorchuk: On the structure of Brauer semigroup and its partial analogue. Problems in Algebra 13 (1998), 29–45.

[10] V. Mazorchuk: Endomorphisms of $n$, ${P}{B}_n$ and $n$. Comm. Algebra 30 (2002), 3489–3513. | MR

Cité par Sources :