Left Regular Representation of Gyrogroups
Keyword(s):
In this article, we examine a subspace L gyr ( G ) of the complex vector space, L ( G ) = { f : f is a function from G to C } , where G is a nonassociative group-like structure called a gyrogroup. The space L gyr ( G ) arises as a representation space for G associated with the left regular representation, consisting of complex-valued functions invariant under certain permutations of G. In the case when G is finite, we prove that dim ( L gyr ( G ) ) = 1 | γ ( G ) | ∑ ρ ∈ γ ( G ) | Fix ( ρ ) | , where γ ( G ) is the subgroup of Sym ( G ) generated by a class of permutations of G and Fix ( ρ ) = { a ∈ G : ρ ( a ) = a } .
1994 ◽
Vol 56
(3)
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pp. 345-383
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2006 ◽
Vol 09
(04)
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pp. 529-546
2009 ◽
Vol 125
(4)
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pp. 2538-2538
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1976 ◽
Vol 28
(6)
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pp. 1311-1319
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A note on holomorphic matric automorphic factors with respect to a lattice in a complex vector space
1976 ◽
Vol 63
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pp. 163-171
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1994 ◽
Vol 36
(3)
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pp. 301-308
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