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Symmetric composition algebras
 J. Algebra
, 1997
"... Abstract. The group gradings on the symmetric composition algebras over arbitrary fields are classified. Applications of this result to gradings on the exceptional simple Lie algebras are considered too. 1. ..."
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Abstract. The group gradings on the symmetric composition algebras over arbitrary fields are classified. Applications of this result to gradings on the exceptional simple Lie algebras are considered too. 1.
THE HERMITIAN LEVEL OF COMPOSITION ALGEBRAS
"... Abstract. The hermitian level of composition algebras with involution over a ring is studied. In particular, it is shown that the hermitian level of a composition algebra with standard involution over a semilocal ring, where two is invertible, is always a power of two when finite. Furthermore, any p ..."
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Abstract. The hermitian level of composition algebras with involution over a ring is studied. In particular, it is shown that the hermitian level of a composition algebra with standard involution over a semilocal ring, where two is invertible, is always a power of two when finite. Furthermore, any
The composition algebra of an affine quiver
, 2004
"... We study the Hall and composition algebras of an affine quiver. In the case of a cyclic quiver, we provide generators for the central polynomial algebra described by Schiffmann and prove that this is in fact the whole of the centre of the Hall algebra. For an affine quiver without oriented cycles, w ..."
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We study the Hall and composition algebras of an affine quiver. In the case of a cyclic quiver, we provide generators for the central polynomial algebra described by Schiffmann and prove that this is in fact the whole of the centre of the Hall algebra. For an affine quiver without oriented cycles
1VALUATIONS ON COMPOSITION ALGEBRAS
"... Necessary and sufficient conditions for a valuation on a field to extend to a central simple nonassociative algebra of finite dimension are obtained. Applications are given to valuations of composition algebras; in particular, we describe all quaternion algebras over the rationals to which the p–adi ..."
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Necessary and sufficient conditions for a valuation on a field to extend to a central simple nonassociative algebra of finite dimension are obtained. Applications are given to valuations of composition algebras; in particular, we describe all quaternion algebras over the rationals to which the p
Homological Algebra of Mirror Symmetry
 in Proceedings of the International Congress of Mathematicians
, 1994
"... Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual Ca ..."
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Cited by 529 (3 self)
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Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual
Factorization in the Composition Algebras
"... Let O be a maximal arithmetic in one of the four (nonsplit) composition algebras over R, and let [ae] = mn be the norm of an element ae in O. Rehm [15] describes an algorithm for finding all factorizations of ae as ae = fffi, where [ff] = m, [fi] = n and (m; n) = 1. Here, we extend the algorithm to ..."
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Let O be a maximal arithmetic in one of the four (nonsplit) composition algebras over R, and let [ae] = mn be the norm of an element ae in O. Rehm [15] describes an algorithm for finding all factorizations of ae as ae = fffi, where [ff] = m, [fi] = n and (m; n) = 1. Here, we extend the algorithm
The Hall And Composition Algebras Of Cyclic Quiver
"... this paper, we assume that k is a field of q elements. THE HALL AND COMPOSITION ALGEBRAS OF CYCLIC QUIVER 3 ..."
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this paper, we assume that k is a field of q elements. THE HALL AND COMPOSITION ALGEBRAS OF CYCLIC QUIVER 3
A Compositional Approach to Performance Modelling
, 1996
"... Performance modelling is concerned with the capture and analysis of the dynamic behaviour of computer and communication systems. The size and complexity of many modern systems result in large, complex models. A compositional approach decomposes the system into subsystems that are smaller and more ea ..."
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Cited by 746 (102 self)
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easily modelled. In this thesis a novel compositional approach to performance modelling is presented. This approach is based on a suitably enhanced process algebra, PEPA (Performance Evaluation Process Algebra). The compositional nature of the language provides benefits for model solution as well
Automating the Design of Graphical Presentations of Relational Information
 ACM Transactions on Graphics
, 1986
"... The goal of the research described in this paper is to develop an applicationindependent presentation tool that automatically designs effective graphical presentations (such as bar charts, scatter plots, and connected graphs) of relational information. Two problems are raised by this goal: The codi ..."
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Cited by 550 (7 self)
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exploits the capabilities of the output medium and the human visual system. A wide variety of designs can be systematically generated by using a composition algebra that composes a small set of primitive graphical languages. Artificial intelligence techniques are used to implement a prototype presentation
Composition algebras over algebraic curves of genus zero
 Trans. Amer. Math. Soc
, 1993
"... Abstract We rephrase the classical theory of composition algebras over fields, particularly the Cayley–Dickson Doubling Process and Zorn’s Vector Matrices, in the setting of locally ringed spaces. Fixing an arbitrary base field, we use these constructions to classify composition algebras over (comp ..."
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Cited by 10 (2 self)
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Abstract We rephrase the classical theory of composition algebras over fields, particularly the Cayley–Dickson Doubling Process and Zorn’s Vector Matrices, in the setting of locally ringed spaces. Fixing an arbitrary base field, we use these constructions to classify composition algebras over
Results 1  10
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206,675