Noncommutative Algebra

Farb, Benson; Dennis, R. Keith

doi:10.1007/978-1-4612-0889-1

Cited by 88 publications

(71 citation statements)

References 2 publications

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“…Suppose now that G = S 8 , the symmetric group on eight letters, and let F be cyclic of order 8. Choose a generator c of F and define an action of F on G by the requirement that the action of c be the conjugation by the 8-cycle τ := (1,2,3,4,5,6,7,8), so that c.σ = τ στ −1 . Now, if g is the 8-cycle (1, 3, 5, 8, 2, 4, 6, 7 Suppose now that Λ [4,2] were central.…”

Section: 7mentioning

confidence: 99%

On higher Frobenius-Schur indicators

Kashina¹,

Sommerhäuser²,

Zhu³

2006

Memoirs of the AMS

105

179

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Section: 7mentioning

confidence: 99%

On higher Frobenius-Schur indicators

Kashina¹,

Sommerhäuser²,

Zhu³

2006

Memoirs of the AMS

105

179

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show abstract

“…Now, let Y be any complete set of inequivalent, irreducible matrix representations for CR n . A naive implementation of the Fourier transform on R n , i.e., computing (12) and (13) directly, gives…”

Section: Computational Complexitymentioning

confidence: 99%

Fast Fourier transforms for the rook monoid

Malandro

Rockmore

2009

Trans. Amer. Math. Soc.

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“…Therefore its compact subsets are exactly its finite subsets. We are now in position to state Jacobson's density theorem (see [8] for a proof). …”

Section: Jacobson's Density Theoremmentioning

confidence: 99%

Linear Induction Algebra and a Normal Form for Linear Operators

Poinsot

2013

Algebraic Informatics

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The set of natural integers is fundamental for at least two reasons: it is the free induction algebra over the empty set (and at such allows definitions of maps by primitive recursion) and it is the free monoid over a one-element set, the latter structure being a consequence of the former. In this contribution, we study the corresponding structure in the linear setting, i.e. in the category of modules over a commutative ring rather than in the category of sets, namely the free module generated by the integers. It also provides free structures of induction algebra and of monoid (in the category of modules). Moreover we prove that each of its linear endomorphisms admits a unique normal form, explicitly constructed, as a non-commutative formal power series.

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Noncommutative Algebra

Cited by 88 publications

References 2 publications

On higher Frobenius-Schur indicators

On higher Frobenius-Schur indicators

Fast Fourier transforms for the rook monoid

Linear Induction Algebra and a Normal Form for Linear Operators

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