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• Borcherds Lie algebra
  ''Borcherds algebra'' ...nberg algebra. Nevertheless, it inherits many of the Kac–Moody properties. Borcherds algebras played a key role in the proof of the [[Moonshine conjectures|Mons
  14 KB (2,218 words) - 10:27, 11 November 2023

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• Weyl-Kac character formula
  ''Weyl–Kac formula, Kac–Weyl character formula, Kac–Weyl formula, Weyl–Kac–Borcherds character formula'' ...Kac–Moody algebras and [[#References|[a2]]] for generalized Kac–Moody (or Borcherds) algebras.
  6 KB (802 words) - 17:43, 1 July 2020
• Borcherds Lie algebra
  ''Borcherds algebra'' ...nberg algebra. Nevertheless, it inherits many of the Kac–Moody properties. Borcherds algebras played a key role in the proof of the [[Moonshine conjectures|Mons
  14 KB (2,218 words) - 10:27, 11 November 2023
• Moonshine conjectures
  ...(cf. also [[Kac–Moody algebra|Kac–Moody algebra]]; [[Borcherds Lie algebra|Borcherds Lie algebra]]). ...rds proved that the $T_g$ obey (a1) by using the denominator identities of Borcherds algebras; the resulting modular equations can be used to prove the Hauptmod
  12 KB (1,765 words) - 09:46, 10 November 2023
• Experimental mathematics
  ...p. 137–143</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> R.E. Borcherds, "What is Moonshine" , ''Proc. Internat. Congress Mathem. (Berlin, 1998)'
  2 KB (333 words) - 22:05, 7 November 2017
• Vertex operator algebra
  The notion of vertex algebra was defined by R. Borcherds [[#References|[a1]]] and is a mathematically precise algebraic counterpart Then Borcherds introduced the axiomatic notion of vertex algebra [[#References|[a1]]] and
  20 KB (2,919 words) - 00:57, 15 February 2024
• Thompson-McKay series
  ...]. The additional structure is that of a [[vertex operator algebra]]. R.E. Borcherds [[#References|[a2]]], [[#References|[a5]]], [[#References|[a17]]] defined a ...a generalized Kac–Moody Lie algebra (GKM Lie algebra), which is defined by Borcherds [[#References|[a3]]] to be a [[Lie algebra|Lie algebra]] $L$ such that:
  21 KB (3,107 words) - 09:12, 10 November 2023
• Fourier coefficients of automorphic forms
  ...a1]]] to refer to the "moonshine" properties of the Monster. In 1998, R.E. Borcherds won the Fields Medal in part because he proved the Conway–Norton "[[moons <tr><td valign="top">[a17]</td> <td valign="top"> R.E. Borcherds, "What is Moonshine" , ''Proc. Internat. Congress Mathem. (Berlin, 1998)''
  13 KB (1,907 words) - 07:36, 22 March 2023
• Vertex operator
  <table><tr><td valign="top">[a1]</td> <td valign="top"> R.E. Borcherds, "Vertex algebras, Kac–Moody algebras, and the monster" ''Proc. Nat. A
  8 KB (1,142 words) - 16:46, 1 July 2020