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lie groups - Lie Algebra of SO (n) - Mathematics Stack Exchange Welcome to the language barrier between physicists and mathematicians Physicists prefer to use hermitian operators, while mathematicians are not biased towards hermitian operators So for instance, while for mathematicians, the Lie algebra $\mathfrak {so} (n)$ consists of skew-adjoint matrices (with respect to the Euclidean inner product on $\mathbb {R}^n$), physicists prefer to multiply them
Fundamental group of the special orthogonal group SO(n) Also, if I'm not mistaken, Steenrod gives a more direct argument in "Topology of Fibre Bundles," but he might be using the long exact sequence of a fibration (which you mentioned)
Prove that the manifold $SO (n)$ is connected The question really is that simple: Prove that the manifold $SO (n) \subset GL (n, \mathbb {R})$ is connected it is very easy to see that the elements of $SO (n
How to find the difference between the sons and mothers age if it . . . A son had recently visited his mom and found out that the two digits that form his age (eg :24) when reversed form his mother's age (eg: 42) Later he goes back to his place and finds out that this whole 'age' reversed process occurs 6 times And if they (mom + son) were lucky it would happen again in future for two more times
What is the relationship between SL (n) and SO (n)? I'm in Linear Algebra right now and we're mostly just working with vector spaces, but they're introducing us to the basic concepts of fields and groups in preparation taking for Abstract Algebra la
semi-simple and simple lie group,SO (n) for n even to moishe yes i know the definition of simple and semi-simple lie group , do you? and by strict definition SO (n) without SO (n) {I,-I} is not semi-simple nor simple, n>1 Then if you do what is a possible proper normal subgroup of SO (4) {I,-I} ?
Diophantus Lifespan - Mathematics Stack Exchange "The son lived exactly half as long as his father" is I think unambiguous Almost nothing is known about Diophantus' life, and there is scholarly dispute about the approximate period in which he lived