[PDF][PDF] Groups with some combinatorial properties
A Hanaki, T Okuyama - 1997 - projecteuclid.org
A Hanaki, T Okuyama
1997•projecteuclid.orgIn [1], E. Bannai introduced the concept of fusion algebras at an algebraic level, a purely
algebraic concept for fusion algebras in mathematical physics. He showed that there exists a
one-to-one correspondence between character algebras (Bose-Mesner algebras at
algebraic level) and fusion algebras at an algebraic level. The concept of character algebras
is a purely algebraic concept for Bose-Mesner algebras of association schemes. For any
commutative association scheme, a character algebra and the corresponding fusion algebra …
algebraic concept for fusion algebras in mathematical physics. He showed that there exists a
one-to-one correspondence between character algebras (Bose-Mesner algebras at
algebraic level) and fusion algebras at an algebraic level. The concept of character algebras
is a purely algebraic concept for Bose-Mesner algebras of association schemes. For any
commutative association scheme, a character algebra and the corresponding fusion algebra …
In [1], E. Bannai introduced the concept of fusion algebras at an algebraic level, a purely algebraic concept for fusion algebras in mathematical physics. He showed that there exists a one-to-one correspondence between character algebras (Bose-Mesner algebras at algebraic level) and fusion algebras at an algebraic level. The concept of character algebras is a purely algebraic concept for Bose-Mesner algebras of association schemes.
For any commutative association scheme, a character algebra and the corresponding fusion algebra at algebraic level are constructed. But this fusion algebra at an algebraic level is far from a fusion algebra in mathematical physics. A fusion algebra in mathematical physics is integral, its matrix 5 is symmetric (and unitary), and it has the modular invariance property. But these are not true for fusion algebras at an algebraic level. So he asked which fusion algebra at an algebraic level have these properties.
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