Presentation of the singular part of the Brauer monoid

Victor Maltcev; Volodymyr Mazorchuk

Mathematica Bohemica (2007)

  • Volume: 132, Issue: 3, page 297-323
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Maltcev, Victor, and Mazorchuk, Volodymyr. "Presentation of the singular part of the Brauer monoid." Mathematica Bohemica 132.3 (2007): 297-323. <http://eudml.org/doc/250259>.

@article{Maltcev2007,
abstract = {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.},
author = {Maltcev, Victor, Mazorchuk, Volodymyr},
journal = {Mathematica Bohemica},
keywords = {semigroup; presentation; symmetric group; Brauer monoid; irreducible systems of generators; idempotents; semigroups; presentations; symmetric groups; Brauer monoids; irreducible systems of generators; idempotents},
language = {eng},
number = {3},
pages = {297-323},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Presentation of the singular part of the Brauer monoid},
url = {http://eudml.org/doc/250259},
volume = {132},
year = {2007},
}

TY - JOUR
AU - Maltcev, Victor
AU - Mazorchuk, Volodymyr
TI - Presentation of the singular part of the Brauer monoid
JO - Mathematica Bohemica
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 132
IS - 3
SP - 297
EP - 323
AB - 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.
LA - eng
KW - semigroup; presentation; symmetric group; Brauer monoid; irreducible systems of generators; idempotents; semigroups; presentations; symmetric groups; Brauer monoids; irreducible systems of generators; idempotents
UR - http://eudml.org/doc/250259
ER -

References

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  2. 10.2307/1968843, Ann. of Math. 38 (1937), 857–872. (1937) Zbl0017.39105MR1503378DOI10.2307/1968843
  3. The Algebraic Theory of Semigroups. Vol. I, Mathematical Surveys, No. 7, American Mathematical Society, Providence, R.I., 1961. (1961) MR0132791
  4. A presentation of the singular part of the symmetric inverse monoid, Preprint, 2004. Zbl1099.20029MR2229484
  5. On conjugation in some transformation and Brauer-type semigroups, Publ. Math. Debrecen 70 (2007), 19–43. (2007) MR2288466
  6. 10.2478/s11533-006-0017-6, Central Europ. J. Math. 4 (2006), 413–434. (2006) MR2233859DOI10.2478/s11533-006-0017-6
  7. 10.1007/s00233-005-0511-3, Semigroup Forum 72 (2006), 223–248. (2006) MR2216091DOI10.1007/s00233-005-0511-3
  8. Generating systems, ideals and the chief series of the Brauer semigroup, Proceedins of Kyiv University, Physical and Mathematical Sciences (2004), 59–65. (2004) 
  9. On the structure of Brauer semigroup and its partial analogue, Problems in Algebra 13 (1998), 29–45. (1998) 
  10. Endomorphisms of n , P B n and n , Comm. Algebra 30 (2002), 3489–3513. (2002) MR1915009

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