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Mathematische Zeitschrift : Volume 286

Mathematische Zeitschrift : Volume 285

Mathematische Zeitschrift : Volume 284

Mathematische Zeitschrift : Volume 284, Issue 3-4, December 2016

Rigid and Schurian modules over cluster-tilted algebras of tame type

Loci of curves with subcanonical points in low genus

Imaginary cones and limit roots of infinite Coxeter groups

A continuous model for quasinilpotent operators

Riesz transforms through reverse Hölder and Poincaré inequalities

On a secant Dirichlet series and Eichler integrals of Eisenstein series

On (2, 4) complete intersection threefolds that contain an Enriques surface

Spectral analysis of the diffusion operator with random jumps from the boundary

Vahlen groups defined over commutative rings

Polynomial inequalities and universal Taylor series

Asymptotic rank of spaces with bicombings

Scaling of conformal blocks and generalized theta functions over $$\overline{\mathcal {M}}_{g,n}$$

Type A images of Galois representations and maximality

Nonintegrability of Hamiltonian system perturbed from integrable system with two singular points

Convergence of the solutions of the discounted equation: the discrete case

Large $${\varvec{p}}^{\prime }$$ -orbits for $${\varvec{p}}$$ -nilpotent linear groups

Slow escaping points of quasiregular mappings

The geometry of Euclidean surfaces with conical singularities

Holomorphic differentials and Laguerre deformation of surfaces

Spectral synthesis for coadjoint orbits of nilpotent Lie groups

Free group representations from vector-valued multiplicative functions, II

On $$L^\infty $$ -BMO estimates for derivatives of the Stokes semigroup

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On $$A_p$$ – $$A_\infty $$ type estimates for square functions

Gevrey smooth topology is proper to detect normalization under Siegel type small divisor conditions

Küchle fivefolds of type c5

Mathematische Zeitschrift : Volume 284, Issue 1-2, October 2016

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Mathematische Zeitschrift : Volume 232

Vahlen groups defined over commutative rings

Content Provider	Springer Nature Link
Author	McInroy, Justin
Copyright Year	2016
Abstract	Elements of a Vahlen group are $$2 \times 2$$ matrices with entries in a Clifford algebra satisfying some conditions. They play a central role in the theory of higher dimensional harmonic automorphic forms. Traditionally they have come in both ordinary and paravector type and have been defined (over Clifford algebras) over the real or complex numbers. We extend the definition of both types to be over a commutative ring with an arbitrary quadratic form. We show that they are indeed groups and identify in each case the group as the pin group, spin group, or another subgroup of the Clifford group. Under some mild conditions, for both types we show the equivalence of our definition with a suitably generalised version of the two standard definitions.
Ending Page	917
Page Count	17
Starting Page	901
File Format	PDF
ISSN	00255874
e-ISSN	14321823
Journal	Mathematische Zeitschrift
Issue Number	3-4
Volume Number	284
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-05-06
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Orthogonal Other matrix groups over rings Clifford algebras, spinors Clifford algebras Mathematics Automorphic forms Vahlen group Commutative rings
Content Type	Text
Resource Type	Article
Subject	Mathematics

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Vahlen groups defined over commutative rings

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