On the faithful representations of Lie groups
نویسندگان
چکیده
منابع مشابه
On Faithful Representations of Lie Groups
where tE:R and I is the unit matrix of degree d. Let GL(K, d) denote the group of all nonsingular matrices of degree d with coefficients in K. Any subgroup of GL(K, d) will be called a linear group of degree d. Let 0 be the identity representation of a linear Lie group G with the Lie algebra 8 so that 9(x) =x (*EG). Then dd is a faithful representation of g and exp dd(X) =0(exp X) =exp X for an...
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We prove an explicit formula for the invariant μ(g) for finite-dimensional semisimple, and reductive Lie algebras g over C. Here μ(g) is the minimal dimension of a faithful linear representation of g. The result can be used to study Dynkin’s classification of maximal reductive subalgebras of semisimple Lie algebras.
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نشان می دهیم که هر اشتقاق لی روی یک c^*-جبر به شکل استاندارد است، یعنی می تواند به طور یکتا به مجموع یک اشتقاق لی و یک اثر مرکز مقدار تجزیه شود. کلمات کلیدی: اشتقاق، اشتقاق لی، c^*-جبر.
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1949
ISSN: 0025-5645
DOI: 10.2969/jmsj/00130254