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Vertex operator algebra
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81	Solutions Chapter 1 1. \|z1 + z2 \|2 + \|z1 − z2 \|2 = (z1 + z2 )(z 1 + z 2 ) + (z1 − z2 )(z 1 − z 2 ) = 2\|z1 \|2 + 2\|z2 \|2 . A diagram similar to Fig[removed]illustrates the geometric interpretation that the sum of the Add to Reading List Source URL: www.math.uiuc.edu Language: English - Date: 2004-07-21 12:19:37 Cauchy–Riemann equations Radius of convergence Vertex operator algebra Residue Mathematical analysis Complex analysis Branch point
82	Putnam Competition Outtake Solutions 1. Let n = m2 + k. If k m, by the binomial theorem, n3/2 = m3 + (3/2)mk + (3/8)m−1 k 2 + O(m−3 k 3 ). Choosing m even and sufficiently large, and (for 0 < α < 1) % $r Add to Reading List Source URL: mlarsen.math.indiana.edu Language: English - Date: 2003-01-18 22:29:02 Operator theory Nonassociative algebra Matrix theory Ordinary differential equations Spectral theory Vertex operator algebra Theorems and definitions in linear algebra Mathematics Mathematical analysis Algebra
83	Computations of elliptic units for real quadratic fields Samit Dasgupta September 20, 2006 Contents 1 Definition of the units Add to Reading List Source URL: people.ucsc.edu Language: English - Date: 2008-09-13 15:52:31 Modular form Symbol P-adic number Valuation Ring of integers Vertex operator algebra Orbifold Abstract algebra Algebra Field theory
84	M M PP EE JJ Mathematical Physics Electronic Journal ISSN[removed]Volume 12, 2006 Paper 4 Add to Reading List Source URL: www.ma.utexas.edu Language: English - Date: 2006-10-05 06:08:35 Operator theory Symbol Vertex operator algebra Grunsky matrix Mathematical analysis Mathematics Complex analysis
85	Supplementary Results for Information Percolation in Segmented Markets Darrell Duffie, Semyon Malamud, and Gustavo Manso November, 2013 Add to Reading List Source URL: www.darrellduffie.com Language: English - Date: 2014-05-31 02:28:37 Operator theory Vertex operator algebra Symbol Mathematical analysis Constructible universe Complex analysis
86	A Monster Lie Algebra? Chapter 30 of “Sphere packing, lattices and groups” by Conway and Sloane, and Adv. in Math[removed]), no. 1, 75–79. R. E. Borcherds, J. H. Conway, L. Queen and N. J. A. Sloane We define a re Add to Reading List Source URL: math.berkeley.edu Language: English - Date: 1999-12-09 18:03:44 Group theory Lie groups Monster Lie algebra Kac–Moody algebra Cartan subalgebra Monster vertex algebra E8 En Vertex operator algebra Abstract algebra Lie algebras Algebra
87	Modular Moonshine II. 24 July 1994, corrected 19 Sept 1995 Duke Math. J[removed]no. 2, [removed]Richard E. Borcherds,∗ Add to Reading List Source URL: math.berkeley.edu Language: English - Date: 1999-12-09 18:08:35 Lie algebras Moonshine theory Conformal field theory Nonassociative algebra Vertex operator algebra Monstrous moonshine Weight Monster vertex algebra Monster Lie algebra Abstract algebra Algebra Mathematics
88	Modular Moonshine III. 11 October 1994, corrected 18 Nov 1997 Duke Math. J[removed]), no. 1, 129–154. Richard E. Borcherds,∗ Add to Reading List Source URL: math.berkeley.edu Language: English - Date: 1999-12-09 18:08:50 Lie algebras Cohomology theories Group theory Conformal field theory Vertex operator algebra Monstrous moonshine Tate cohomology group XTR Group cohomology Abstract algebra Algebra Homological algebra
89	The monster Lie algebra. Adv. Math. Vol 83, No. 1, September 1990, p[removed]Richard E. Borcherds, Department of pure mathematics and mathematical statistics, 16 Mill Lane, Cambridge CB2 1SB, England. We calculate the mu Add to Reading List Source URL: math.berkeley.edu Language: English - Date: 1999-12-09 18:06:24 Lie algebras Moonshine theory Representation theory of Lie groups Quadratic forms Lie groups Monster Lie algebra Kac–Moody algebra Vertex operator algebra Weight Abstract algebra Algebra Mathematics
90	Introduction to the monster Lie algebra. Groups, Combinatorics, and geometry, p. 99–107, edited by M. W. Liebeck and J. Saxl, L.M.S. lecture note series 165, C.U.P[removed]Richard E. Borcherds, I would like to thank J. Add to Reading List Source URL: math.berkeley.edu Language: English - Date: 1999-12-09 18:08:25 Monster Lie algebra Kac–Moody algebra Weyl character formula Monstrous moonshine Simple Lie group Vertex operator algebra En Representation theory E8 Abstract algebra Lie algebras Lie groups

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