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Description
Abstract Lie AlgebrasSolid but concise, this account of Lie algebra emphasizes the theory's simplicity and offers new approaches to major theorems. Author David J. Winter, a Professor of Mathematics at the University of Michigan, also presents a general, extensive treatment of Cartan and related Lie subalgebras over arbitrary fields. Preliminary material covers modules and nonassociate algebras, followed by a compact, self contained development of the theory of Lie
Solid but concise, this account of Lie algebra emphasizes the theory's simplicity and offers new approaches to major theorems. Author David J. Winter, a Professor of Mathematics at the University of Michigan, also presents a general, extensive treatment of Cartan and related Lie subalgebras over arbitrary fields.Preliminary material covers modules and nonassociate algebras, followed by a compact, self-contained development of the theory of Lie algebras of characteristic 0. Topics include solvable and nilpotent Lie algebras, Cartan subalgebras, and Levi's radical splitting theorem and the complete reducibility of representations of semisimple Lie algebras. Additional subjects include the isomorphism theorem for semisimple Lie algebras and their irreducible modules, automorphism of Lie algebras, and the conjugacy of Cartan subalgebras and Borel subalgebras. An extensive theory of Cartan and related subalgebras of Lie algebras over arbitrary fields is developed in the final chapter, and an appendix offers background on the Zariski topology.
Binding Type: Paperback
Publisher: Dover Publications
Published: 01/11/2008
ISBN: 9780486462820
Pages: 150
Weight: 0.37lbs
Size: 8.41h x 5.52w x 0.31d
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4.6 ★★★★★
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Product Reviews
★★★★★ 5
Great sock liners
Size: Medium, Color: (001) Black / Black / Pitch Gray
Awesome socks. Has little gel pad on top of heel for no slip. Thin and comfortable. Previously Purchased at Nordstrom rack and no longer in stock. Happy to find here
Note: Will shrink a little best to air dry
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Reviewed in the United States on April 16, 2026
★★★★★ 5
Very good product
Size: Medium, Color: (001) Black / Black / Pitch Gray
I purchased these to wear inside lowcut slip on casual shoes, I don't particularly like to not wear socks in my shoes for hygienic reasons. Prior to purchasing these socks, all I could find were those made of very light beige hosiery type material , and my slip on shoes would slide around a bit. These are light weight and breathable athletic type material, with a very good gripper strip at the heel. One pair of my slip on casual shoes have a particularly lower cut in the toe area, but the shoe is black and I chose the black color and though I see a hint of the sock there, it matches and does not detract from the look of the casual solid black shoe
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Reviewed in the United States on May 15, 2026
★★★★★ 5
They stay out! No more sock wads!
Size: Medium, Color: (100) White / White / Mod Gray
Best no show socks ever made!!!!! I've been struggling for 2 years to find ones that actually stay on your foot, even other national brands, and I just became content wearing my sneakers without socks. They ALWAYS slid down into my show & I ended up walking on a wad of sock until I could fix it...or usually just took them off after a couple of tries. Enter Under Armor!!! They a mid weight, but not very thick & still breathable. They work too by actually staying on your foot! Not once have they slid down into my show!! Very comfortable but they could be a little more affordable.
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Reviewed in the United States on August 1, 2025
★★★★★ 5
Love!
Size: Large, Color: (100) White / White / Mod Gray
Ive tried so many no show socks but I love these. This is the 3rd set I've bought. They never slip off and the material is thin and breathable. Perfect for working out.
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Reviewed in the United States on March 2, 2026
★★★★★ 5
True no-show socks that don’t slide down!
Size: Medium, Color: (100) White / White / Mod Gray, Size: Medium, Color: (100) White / White / Mod Gray
This is the first pair of no-show socks I’ve tried that actually don’t slide down into my shoes. Trust me… I have tried lots of different pairs and this is the one! They fit perfectly. They’re not too thick and they’re obviously durable because I wash them after each wear, so daily.
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Reviewed in the United States on March 21, 2026