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2022
In this chapter, we establish some basic facts on Clifford theory for induced representations from a normal subgroup and we give the first applications of the theory.
Ceccherini-Silberstein T. +2 more
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In this chapter, we establish some basic facts on Clifford theory for induced representations from a normal subgroup and we give the first applications of the theory.
Ceccherini-Silberstein T. +2 more
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Advances in Applied Clifford Algebras, 2021
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P. Cerejeiras, M. Vajiac
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
P. Cerejeiras, M. Vajiac
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Acta Mathematica Hungarica, 2002
Let \(R\) be an associative ring and let \((R,\circ)\) be the adjoint semigroup of \(R\), where \(a\circ b=a+b-ab\) for \(a,b\in R\). This paper continues the authors' investigations into the relationship between a ring and its adjoint semigroup [\textit{H. Heatherly} and \textit{R. P. Tucci}, Acta Math. Hung. 90, No. 3, 231-242 (2001; Zbl 0973.20059)].
Heatherly, Henry, Tucci, Ralph P.
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Let \(R\) be an associative ring and let \((R,\circ)\) be the adjoint semigroup of \(R\), where \(a\circ b=a+b-ab\) for \(a,b\in R\). This paper continues the authors' investigations into the relationship between a ring and its adjoint semigroup [\textit{H. Heatherly} and \textit{R. P. Tucci}, Acta Math. Hung. 90, No. 3, 231-242 (2001; Zbl 0973.20059)].
Heatherly, Henry, Tucci, Ralph P.
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Clifford Algebras and Clifford Modules
1993We study bundles over a point, recalling the definition of the Clifford algebra Cl(V, q) of a real vector space V of dimension m equipped with a positive definite inner product q; the ℤ2-grading of Clifford algebras is shown, followed by an introduction of complex representations of Clifford algebras and the concept of complex Cl(V, q)-modules and of ...
Bernhelm Booß-Bavnbek +1 more
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On Clifford neurons and Clifford multi-layer perceptrons
Neural Networks, 2008We study the framework of Clifford algebra for the design of neural architectures capable of processing different geometric entities. The benefits of this model-based computation over standard real-valued networks are demonstrated. One particular example thereof is the new class of so-called Spinor Clifford neurons.
Buchholz, Sven, Sommer, Gerald
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The Annals of Mathematics, 1970
Let G be a group, N be a normal subgroup of G, and p be an irreducible (finite-dimensional) character of N in some algebraically closed field a. Assume that the stabilizer G, of p in G has finite index in G. Then Clifford's theory [2] gives us a central extension G of the multiplicative group F of a by GIN together with a one-to-one correspondence ...
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Let G be a group, N be a normal subgroup of G, and p be an irreducible (finite-dimensional) character of N in some algebraically closed field a. Assume that the stabilizer G, of p in G has finite index in G. Then Clifford's theory [2] gives us a central extension G of the multiplicative group F of a by GIN together with a one-to-one correspondence ...
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