TY - JOUR

T1 - COXETER COVERS OF THE CLASSICAL COXETER GROUPS

AU - MEIRAV, AMRAM

AU - ROBERT, SHWARTZ

AU - Teicher, M.

PY - 2010

Y1 - 2010

N2 - et C(T) be a generalized Coxeter group, which has a natural map onto one of the classical Coxeter groups, either Bn or Dn. Let CY(T) be a natural quotient of C(T), and if C(T) is simply-laced (which means all the relations between the generators has order 2 or 3), CY(T) is a generalized Coxeter group, too. Let At,n be a group which contains t Abelian groups generated by n elements. The main result in this paper is that CY(T) is isomorphic to At,n ⋊ Bn or At,n ⋊ Dn, depends on whether the signed graph T contains loops or not, or in other words C(T) is simply-laced or not, and t is the number of the cycles in T. This result extends the results of Rowen, Teicher and Vishne to generalized Coxeter groups which have a natural map onto one of the classical Coxeter groups.
Read More: http://www.worldscientific.com/doi/abs/10.1142/S0218196710006023

AB - et C(T) be a generalized Coxeter group, which has a natural map onto one of the classical Coxeter groups, either Bn or Dn. Let CY(T) be a natural quotient of C(T), and if C(T) is simply-laced (which means all the relations between the generators has order 2 or 3), CY(T) is a generalized Coxeter group, too. Let At,n be a group which contains t Abelian groups generated by n elements. The main result in this paper is that CY(T) is isomorphic to At,n ⋊ Bn or At,n ⋊ Dn, depends on whether the signed graph T contains loops or not, or in other words C(T) is simply-laced or not, and t is the number of the cycles in T. This result extends the results of Rowen, Teicher and Vishne to generalized Coxeter groups which have a natural map onto one of the classical Coxeter groups.
Read More: http://www.worldscientific.com/doi/abs/10.1142/S0218196710006023

UR - http://www.worldscientific.com/doi/abs/10.1142/S0218196710006023

M3 - Article

SN - 0218-1967

VL - 20

SP - 1041

EP - 1062

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

IS - 8

ER -