Pseudofunctors on Modules with Zero Dimensional Support
Pseudofunctors on Modules with Zero Dimensional Support

Author: I-Chiau Huang

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 73

ISBN-13: 0821826085

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Pseudofunctors with values on modules with zero dimensional support are constructed over the formally smooth category and residually finite category. Combining those pseudofunctors, a pseudofunctor over the category whose objects are Noetherian local rings and whose morphisms are local with finitely generated residue field extensions is constructed.

Variance and Duality for Cousin Complexes on Formal Schemes
Variance and Duality for Cousin Complexes on Formal Schemes

Author: Joseph Lipman

Publisher: American Mathematical Soc.

Published: 2005

Total Pages: 290

ISBN-13: 0821837052

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Robert Hartshorne's book, Residues and Duality (1966, Springer-Verlag), introduced the notion of residual complexes and developed a duality theory (Grothendieck duality) on the category of maps of noetherian schemes. The three articles in this volume constitute a reworking of the main parts of the corresponding chapters in Hartshorne's 1966 book in greater generality using a somewhat different approach. In particular, throughout this volume, the authors work with arbitrary (quasi-coherent, torsion) Cousin complexes on formal schemes, not only with residual complexes on ordinary schemes. Additionally, their motivation is to help readers gain a better understanding of the relation between local properties of residues and global properties of the dualizing pseudofunctor. The book is suitable for graduate students and researchers working in algebraic geometry.

Analytic Deformations of the Spectrum of a Family of Dirac Operators on an Odd-Dimensional Manifold with Boundary
Analytic Deformations of the Spectrum of a Family of Dirac Operators on an Odd-Dimensional Manifold with Boundary

Author: Paul Kirk

Publisher: American Mathematical Soc.

Published: 1996

Total Pages: 73

ISBN-13: 082180538X

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The analytic perturbation theory for eigenvalues of Dirac operators on odd dimensional manifolds with boundary is described in terms of [italic]extended L2 eigenvectors [end italics] on manifolds with cylindrical ends. These are generalizations of the Atiyah-Patodi-Singer extended [italic capital]L2 kernel of a Dirac operator. We prove that they form a discrete set near zero and deform analytically, in contrast to [italic capital]L2 eigenvectors, which can be absorbed into the continuous spectrum under deformations when the tangential operator is not invertible. We show that the analytic deformation theory for extended [italic capital]L2 eigenvectors and Atiyah-Patodi-Singer eigenvectors coincides.

Completely Positive Hypergroup Actions
Completely Positive Hypergroup Actions

Author: Ajit Iqbal Singh

Publisher: American Mathematical Soc.

Published: 1996

Total Pages: 87

ISBN-13: 0821805398

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It is now well know that the measure algebra [script capital]M([italic capital]G) of a locally compact group can be regarded as a subalgebra of the operator algebra [italic capital]B([italic capital]B([italic capital]L2([italic capital]G))) of the operator algebra [italic capital]B([italic capital]L2([italic capital]G)) of the Hilbert space [italic capital]L2([italic capital]G). We study the situation in hypergroups and find that, in general, the analogous map for them is neither an isometry nor a homomorphism. However, it is completely positive and completely bounded in certain ways. This work presents the related general theory and special examples.

Stratifying Endomorphism Algebras
Stratifying Endomorphism Algebras

Author: Edward Cline

Publisher: American Mathematical Soc.

Published: 1996

Total Pages: 135

ISBN-13: 082180488X

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This paper presents a systematic study of the relationships between the representation theories of [italic capital]R and [italic capital]A, especially those involving actual or potential quasi-hereditary structures on the latter algebra. Our original motivation comes from the theory of Schur algebras, work of Soergel on the Bernstein-Gelfand-Gelfand category [script capital]O, and resent results of Dlab-Heath-Marko realizing certain endomorphism algebras as quasi-hereditary algebras. We synthesize common features of all these examples, and go beyond them in a number of new directions.

The Index Theorem for Minimal Surfaces of Higher Genus
The Index Theorem for Minimal Surfaces of Higher Genus

Author: Friedrich Tomi

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 90

ISBN-13: 0821803522

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In this paper we formulate and prove an index theorem for minimal surfaces of higher topological type spanning one boundary contour. Our techniques carry over to surfaces with several boundary contours as well as to unoriented surfaces.

Triangular Algebras and Ideals of Nest Algebras
Triangular Algebras and Ideals of Nest Algebras

Author: John Lindsay Orr

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 65

ISBN-13: 0821804057

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Immersive environments such as virtual reality technology makes possible can respond to their audiences, so that each person's experience of the environment is unique. This volume brings together 11 essays along with artists' projects produced at the Banff Centre for the Arts in Canada to explore issues raised by the creation of virtual environments. The essays approach the social and cultural implications of cyberspace from the perspective of cultural studies, communications, art history, art criticism, English, and women's studies; while artists who created nine virtual worlds at the Banff Centre discuss what they have tried to accomplish in both theoretical and technical terms. With 64 illustrations, including 18 color plates. Annotation copyright by Book News, Inc., Portland, OR

Two-Generator Discrete Subgoups of $PSL(2, R)$
Two-Generator Discrete Subgoups of $PSL(2, R)$

Author: Jane Gilman

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 221

ISBN-13: 0821803611

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The discreteness problem is the problem of determining whether or not a two-generator subgroup of $PSL(2, R)$ is discrete. Historically, papers on this old and subtle problem have been known for their errors and omissions. This book presents the first complete geometric solution to the discreteness problem by building upon cases previously presented by Gilman and Maskit and by developing a theory of triangle group shinglings/tilings of the hyperbolic plane and a theory explaining why the solution must take the form of an algorithm. This work is a thoroughly readable exposition that captures the beauty of the interplay between the algebra and the geometry of the solution.

Classification of Direct Limits of Even Cuntz-Circle Algebras
Classification of Direct Limits of Even Cuntz-Circle Algebras

Author: Huaxin Lin

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 129

ISBN-13: 0821804030

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We prove a classification theorem for purely infinite C∗-algebras that is strong enough to show that the tensor products of two different irrational rotation algebras with the same even Cuntz algebra are isomorphic.

Degenerate Principal Series for Symplectic and Odd-Orthogonal Groups
Degenerate Principal Series for Symplectic and Odd-Orthogonal Groups

Author: Chris Jantzen

Publisher: American Mathematical Soc.

Published: 1996-01-01

Total Pages: 114

ISBN-13: 0821804820

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This memoir studies reducibility in a certain class of induced representations for and , where is -adic. In particular, it is concerned with representations obtained by inducing a one-dimensional representation from a maximal parabolic subgroup (i.e., degenerate principal series representations). Using the Jacquet module techniques of Tadić, the reducibility points for such representations are determined. When reducible, the composition series is described, giving Langlands data and Jacquet modules for the irreducible composition factors.