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Books on the topic 'Semisimple algebraic groups'

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Published: 21 September 2024

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1

Humphreys, James E. Conjugacy classes in semisimple algebraic groups. Providence, R.I: American Mathematical Society, 1995.

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2

Hiss, G. Imprimitive irreducible modules for finite quasisimple groups. Providence, Rhode Island: American Mathematical Society, 2015.

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3

Kapovich, Michael. The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra. Providence, R.I: American Mathematical Society, 2008.

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4

1959-, McGovern William M., ed. Nilpotent orbits in semisimple Lie algebras. New York: Van Nostrand Reinhold, 1993.

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5

Doran, Robert S., 1937- editor of compilation, Friedman, Greg, 1973- editor of compilation, and Nollet, Scott, 1962- editor of compilation, eds. Hodge theory, complex geometry, and representation theory: NSF-CBMS Regional Conference in Mathematics, June 18, 2012, Texas Christian University, Fort Worth, Texas. Providence, Rhode Island: American Mathematical Society, 2013.

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6

1938-, Griffiths Phillip, and Kerr Matthew D. 1975-, eds. Hodge theory, complex geometry, and representation theory. Providence, Rhode Island: Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, 2013.

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7

Benkart, Georgia. Stability in modules for classical lie algebras: A constructive approach. Providence, R.I., USA: American Mathematical Society, 1990.

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8

Strade, Helmut, Thomas Weigel, Marina Avitabile, and Jörg Feldvoss. Lie algebras and related topics: Workshop in honor of Helmut Strade's 70th birthday : lie algebras, May 22-24, 2013, Università degli studi di Milano-Bicocca, Milano, Italy. Providence, Rhode Island: American Mathematical Society, 2015.

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9

Humphreys, James E. Conjugacy Classes in Semisimple Algebraic Groups. American Mathematical Society, 1995.

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10

Gille, Philippe. Groupes algébriques semi-simples en dimension cohomologique ≤2: Semisimple algebraic groups in cohomological dimension ≤2. Springer, 2019.

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11

Brauer groups, Tamagawa measures, and rational points on algebraic varieties. Providence, Rhode Island: American Mathematical Society, 2014.

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12

Collingwood, David H., and William M. McGovern. Nilpotent Orbits In Semisimple Lie Algebra: An Introduction. Chapman & Hall/CRC, 1993.

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13

Unramified Brauer Group and Its Applications. American Mathematical Society, 2018.

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14

Dobrev, Vladimir K. Noncompact Semisimple Lie Algebras and Groups. de Gruyter GmbH, Walter, 2016.

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15

Dobrev, Vladimir K. Noncompact Semisimple Lie Algebras and Groups. de Gruyter GmbH, Walter, 2016.

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16

Dobrev, Vladimir K. Noncompact Semisimple Lie Algebras and Groups. de Gruyter GmbH, Walter, 2016.

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17

Donkin, S. Representations of the Hyperalgebra of a Semisimple Group. Cambridge University Press, 2008.

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18

Semisolvability of Semisimple Hopf Algebras of Low Dimension (Memoirs of the American Mathematical Society). American Mathematical Society, 2007.

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19

Onishchik, Arkady L. Lectures on Real Semisimple Lie Algebras and Their Representations (ESI Lectures in Mathematics & Physics). Amer Mathematical Society, 2004.

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20

Gaitsgory, Dennis, and Jacob Lurie. Weil's Conjecture for Function Fields. Princeton University Press, 2019. http://dx.doi.org/10.23943/princeton/9780691182148.001.0001.

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A central concern of number theory is the study of local-to-global principles, which describe the behavior of a global field K in terms of the behavior of various completions of K. This book looks at a specific example of a local-to-global principle: Weil's conjecture on the Tamagawa number of a semisimple algebraic group G over K. In the case where K is the function field of an algebraic curve X, this conjecture counts the number of G-bundles on X (global information) in terms of the reduction of G at the points of X (local information). The goal of this book is to give a conceptual proof of Weil's conjecture, based on the geometry of the moduli stack of G-bundles. Inspired by ideas from algebraic topology, it introduces a theory of factorization homology in the setting ℓ-adic sheaves. Using this theory, the authors articulate a different local-to-global principle: a product formula that expresses the cohomology of the moduli stack of G-bundles (a global object) as a tensor product of local factors. Using a version of the Grothendieck–Lefschetz trace formula, the book shows that this product formula implies Weil's conjecture. The proof of the product formula will appear in a sequel volume.
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21

Noncommutative geometry and global analysis: Conference in honor of Henri Moscovici, June 29-July 4, 2009, Bonn, Germany. Providence, R.I: American Mathematical Society, 2011.

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