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A note on representation of positive definite binary quadratic forms by positive definite quadratic forms in 6 variables

Yoshiyuki Kitaoka (1990)

Acta Arithmetica

A Remark on Quadratic Spaces over Noncommutative Semilocal Rings.

Bernhard Keller (1988)

Mathematische Zeitschrift

A tutorial on conformal groups

Ian Porteous (1996)

Banach Center Publications

Our concern is with the group of conformal transformations of a finite-dimensional real quadratic space of signature (p,q), that is one that is isomorphic to $ℝ^{p, q}$ , the real vector space $ℝ^{p + q}$ , furnished with the quadratic form $x^{(2)} = x \cdot x = - x_{1}^{2} - x_{2}^{2} - . . . - x_{p}^{2} + x_{p + 1}^{2} + . . . + x_{p + q}^{2}$ , and especially with a description of this group that involves Clifford algebras.

Clifford algebras, Möbius transformations, Vahlen matrices, and $B$ -loops

Jimmie Lawson (2010)

Commentationes Mathematicae Universitatis Carolinae

In this paper we show that well-known relationships connecting the Clifford algebra on negative euclidean space, Vahlen matrices, and Möbius transformations extend to connections with the Möbius loop or gyrogroup on the open unit ball $B$ in $n$ -dimensional euclidean space $ℝ^{n}$ . One notable achievement is a compact, convenient formula for the Möbius loop operation $a * b = (a + b) {(1 - a b)}^{- 1}$ , where the operations on the right are those arising from the Clifford algebra (a formula comparable to $(w + z) {(1 + \bar{w} z)}^{- 1}$ for the Möbius loop multiplication...

Compositions of quadratic forms with quadratic, bilinear or Hermitian forms.

Züger, Remo (1999)

Beiträge zur Algebra und Geometrie

Cycles of isotropic subspaces and formulas for symmetric degeneracy loci

Piotr Pragacz (1990)

Banach Center Publications

Discriminant algebras and adjoints of quadratic forms.

Loos, Ottmar (1997)

Beiträge zur Algebra und Geometrie

Factoring biquadratic maps on modules.

Bruce R. Ebanks (1995)

Forum mathematicum

Graded algebra automorphisms.

Montse Vela (1998)

Collectanea Mathematica

Indecomposable Rank 4 Quadratic Spaces of Non-Trivial Discriminant Over Polynomial Rings.

Raman Parimala, Raman Sridharan (1983)

Mathematische Zeitschrift

Invariants of orthogonal $G$ -modules from the character table.

Nebe, Gabriele (2000)

Experimental Mathematics

Motivic cohomology and unramified cohomology of quadrics

Bruno Kahn, R. Sujatha (2000)

Journal of the European Mathematical Society

This is the last of a series of three papers where we compute the unramified cohomology of quadrics in degree up to 4. Complete results were obtained in the two previous papers for quadrics of dimension $\leq 4$ and $\geq 11$ . Here we deal with the remaining dimensions between 5 and 10. We also prove that the unramified cohomology of Pfister quadrics with divisible coefficients always comes from the ground field, and that the same holds for their unramified Witt rings. We apply these results to real quadrics....

On compositions and triality.

R. Sridharan, M.-A. Knus, R. Parimala (1994)

Journal für die reine und angewandte Mathematik

On integral representations by totally positive ternary quadratic forms

Elise Björkholdt (2000)

Journal de théorie des nombres de Bordeaux

Let $K$ be a totally real algebraic number field whose ring of integers $R$ is a principal ideal domain. Let $f (x_{1}, x_{2}, x_{3})$ be a totally definite ternary quadratic form with coefficients in $R$ . We shall study representations of totally positive elements $N \in R$ by $f$ . We prove a quantitative formula relating the number of representations of $N$ by different classes in the genus of $f$ to the class number of $R [\sqrt{- c_{f} N}]$ , where $c_{f} \in R$ is a constant depending only on $f$ . We give an algebraic proof of a classical result of H. Maass on representations...

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