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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Summer 2016 • Question 3

Question

Math 6510 • Differentiable Manifolds Summer 2016 • Question 3

Give a sketch of the calculation that the Lie bracket on the Lie algebra of \(\mathrm {GL}_n(\mathbb {R})\), identified with the space of all \(n\times n\) matrices, is \([A,B]=AB-BA\).

Raw LaTeX

Give a sketch of the calculation that the Lie bracket on the Lie algebra
of \(\mathrm{GL}_n(\R)\), identified with the space of all \(n\times n\) matrices,
is \([A,B]=AB-BA\).

Topic Tags

Lie Algebras and Exponential Maps