Constructing a Lie group analog for the Monster Lie algebra
نویسندگان
چکیده
Let $$\mathfrak {m}$$ be the Monster Lie algebra. We summarize several interrelated constructions of group analogs for . Our are Chevalley and Kac–Moody groups their generators relations.
منابع مشابه
A Monster Lie Algebra ?
We define a remarkable Lie algebra of infinite dimension, and conjecture that it may be related to the Fischer-Griess Monster group. The idea was mooted in [C-N] that there might be an infinite-dimensional Lie algebra (or superalgebra) L that in some sense “explains” the Fischer-Griess ‘Monster” group M . In this chapter we produce some candidates for L based on properties of the Leech lattice ...
متن کاملIntroduction to the Monster Lie Algebra
for each element g of the monster, so that our problem is to work out what these Thompson series are. For example, if 1 is the identity element of the monster then Tr(1|Vn) = dim(Vn) = c(n), so that the Thompson series T1(q) = j(τ) − 744 is the elliptic modular function. McKay, Thompson, Conway and Norton conjectured [Con] that the Thompson series Tg(q) are always Hauptmoduls for certain modula...
متن کاملA Bound for the Nilpotency Class of a Lie Algebra
In the present paper, we prove that if L is a nilpotent Lie algebra whose proper subalge- bras are all nilpotent of class at most n, then the class of L is at most bnd=(d 1)c, where b c denotes the integral part and d is the minimal number of generators of L.
متن کاملWhat Does a Lie Algebra Know about a Lie Group?
We define Lie groups and Lie algebras and show how invariant vector fields on a Lie group form a Lie algebra. We prove that this correspondence respects natural maps and discuss conditions under which it is a bijection. Finally, we introduce the exponential map and use it to write the Lie group operation as a function on its Lie algebra.
متن کاملUniversity of Cambridge Approximating the Exponential from a Lie Algebra to a Lie Group Approximating the Exponential from a Lie Algebra to a Lie Group
Consider a diierential equation y 0 = A(t; y)y; y(0) = y0 with y0 2 G and A : R + G ! g, where g is a Lie algebra of the matricial Lie group G. Every B 2 g can be mapped to G by the matrix exponential map exp (tB) with t 2 R. Most numerical methods for solving ordinary diierential equations (ODEs) on Lie groups are based on the idea of representing the approximation yn of the exact solution y(t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Letters in Mathematical Physics
سال: 2022
ISSN: ['0377-9017', '1573-0530']
DOI: https://doi.org/10.1007/s11005-022-01531-4