UNITARY UNITS IN GROUP ALGEBRAS AND FIBONACCI SEQUENCES.
- Resource Type
- Article
- Authors
- VIEIRA, ANA C.; DA SILVA, VIVIANE RIBEIRO T.
- Source
- Journal of Algebra & Its Applications. Apr2006, Vol. 5 Issue 2, p145-151. 7p.
- Subject
- *GROUP algebras
*FIBONACCI sequence
*CAYLEY algebras
*ABELIAN groups
*LOCALLY compact groups
- Language
- ISSN
- 0219-4988
Let * denote the canonical involution of the group algebra KG induced by the map x ↦ x-1 for x ∈ G. In case K is a real extension of ℚ, we consider Cayley unitary elements built out of skew elements k = α(x - x-1) in KG such that 1 + k is invertible in KG, for α ∈ K and x ∈ G. The constructions involve an interesting sequence in the coefficients of (1 + k)-1 which is the Fibonacci sequence when α = 1. [ABSTRACT FROM AUTHOR]