Krammer's Representation of the Pure Braid Group, P3. (27th June 2010)

• Record Type: Journal Article
• Authors: Abdulrahim, Mohammad N.; Al-Tahan, Madline
• Other Names: Bell Howard Academic Editor.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 2010(2010)
• Publication Date: 2010-06-27
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1155/2010/806502
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : We consider Krammer's representation of the pure braid group on three strings: P 3 → G L ( 3, Z [ t ± 1, q ± 1 ] ), where t and q are indeterminates. As it was done in the case of the braid group, B 3, we specialize the indeterminates t and q to nonzero complex numbers. Then we present our main theorem that gives us a necessary and sufficient condition that guarantees the irreducibility of the complex specialization of Krammer's representation of the pure braid group, P 3 .