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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 ★★★★★
Based on 9 reviews
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Product Reviews
★★★★★ 5
This was another great purchase 10 out of 10 would recommend
Color: Brown, Pattern Name: Tree stump 2 Pack
Worth the price! This is something my dog absolutely loves that keeps her engaged it's so easy to clean it's safe the size is just right for her and it's hard enough to where I don't have to worry about it breaking or her chewing it up or something.Great Buy
WAS THIS REVIEW HELPFUL?YesReportShare
Reviewed in the United States on May 6, 2026
★★★★★ 5
High quality toy loved by my dogs
Color: Brown, Pattern Name: Tree stump 2 Pack
These are amazing, my dogs favorite toys now. I have two strong chewers who haven’t been able to destroy these. I use yogurt, peanut butter and eggs, broth, really any dog friendly liquids to fill it. I recommend these to all my friends and family with dogs of all sizes.
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Reviewed in the United States on June 5, 2026
★★★★★ 5
Excellent Purchase!
Color: Brown, Pattern Name: Tree stump 2 Pack, Color: Brown, Pattern Name: Tree stump 2 Pack
My dogs and I really like these treat toys! I was surprised and questioning whether to keep them when I took them from the box. They are heavier and harder and larger than I envisioned. I didn't realize how hard a nylon/coffee wood combo actually is. However, I want to emphasize that the sales description IS accurate. It details the specifications, materials and size. Clearly states that they are designed specifically for aggressive chewers. I just haven't purchased anything quite like this before.
That said, I was happy it came in a 2 pack and it seems a good value for the price. The dogs have chewed on them, I can see the marks, but they haven't made a dent after about 6 treat sessions. These logs are at least as hard as antlers. They will last a long time. The silicone trays are easy to fill and freeze. I made low calorie popsicles with bone broth and some added mix-ins like pureed pumpkin, healthy freeze dried dog food topper sprinkle, etc. You could also add some peanut butter in the small open end of the log if you want. I just ran hot water over the bottom of the silicone tray to melt the freeze slightly and the frozen treats slid right out. They are shaped perfectly to fit the hole in the log. The seller provided small tools to unscrew/screw the cap in and out for filling with treats.
Even the smaller of my 2 dogs (30 lb Brittany) can get her mouth around the end of the log to carry it to her bed to lay and lick/chew it. I guess another advantage, beyond the durability, of the material is that my dogs don't want to play with it like a toy. They know it is time to relax and have a treat timeout. More like chilling with a chew bone.
Overall we really do love these!! Glad I tried them.
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Reviewed in the United States on January 25, 2026
★★★★★ 5
Great Product!
Size: Medium, Color: green, orange, pink, Pattern Name: clean tuff bone bacon
My dogs love their dental chews! This product is durable and the perfect size for each of my dogs. I've purchased two of them (medium and large). One of my dogs is an aggressive chewer and this product is holding up. Hartz makes great pet products. I'm very happy with the product.
WAS THIS REVIEW HELPFUL?YesReportShare
Reviewed in the United States on March 30, 2026
★★★★★ 5
Good quality
Size: Extra Small, Color: blue, purple, Pattern Name: clean tuff bone bacon
My dogs favorite toy. It’s so small and cute lol it’s lightweight and easy for her to chew. The quality is great, it’s lasting and no broken pieces.
WAS THIS REVIEW HELPFUL?YesReportShare
Reviewed in the United States on March 18, 2026
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