Show that for any two finite-dimensional L-representations V and W of L: (a) Hom (V, k) ~V* as L-modules. (What should the action of L on k be?) (b) Hom (V, W) ~V* ®W as L-modules (the tensor product is the tensor product of L-modules)
Show that for any two finite-dimensional L-representations V and W of L: (a) Hom (V, k) ~V* as L-modules. (What should the action of L on k be?) (b) Hom (V, W) ~V* ®W as L-modules (the tensor product is the tensor product of L-modules)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Help solve part b of this lie algebra question. Thank you.
Transcribed Image Text:Show that for any two finite-dimensional L-representations V and W of L:
(a) Hom (V, k) ~ V* as L-modules. (What should the action of L on k be?)
(b) Hom (V, W) ~V* ® W as L-modules (the tensor product is the tensor product
of L-modules)
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