£33.95
FREE Delivery in the UK.
Only 1 left in stock (more on the way).
Dispatched from and sold by Amazon.
Gift-wrap available.
Quantity:1
Essays in the History of ... has been added to your Basket
Have one to sell?
Flip to back Flip to front
Listen Playing... Paused   You're listening to a sample of the Audible audio edition.
Learn more
See this image

Essays in the History of Lie Groups and Algebraic Groups (History of Mathematics) Hardcover – 20 Sep 2001


See all formats and editions Hide other formats and editions
Amazon Price New from Used from
Hardcover
"Please retry"
£33.95
£24.98 £27.43
£33.95 FREE Delivery in the UK. Only 1 left in stock (more on the way). Dispatched from and sold by Amazon. Gift-wrap available.


Product details


More About the Author

Discover books, learn about writers, and more.

Customer Reviews

There are no customer reviews yet on Amazon.co.uk.
5 star
4 star
3 star
2 star
1 star

Most Helpful Customer Reviews on Amazon.com (beta)

Amazon.com: 1 review
1 of 3 people found the following review helpful
An extended abstract of Lie theory after Sophus Lie 2 Sep 2013
By flashgordon - Published on Amazon.com
Format: Hardcover Verified Purchase
Not that Armand doesn't mention that Sophus Lie's initial effort was to make a unified closed form solution to differential equations, but if you want to know about that mathematics, you have to go somewhere else - such as Thomas Hawkins; a book I'm hoping to get to soon enough next.

Armand Borel's book treats of Elie Cartan's differential geometry in terms of Sophus's Lie's work, then Hermann Weyl's Lie algebra work; the interplay between Lie algebra's and Lie groups; global and local aspects. Then there's Chevelley's algebraic groups; algebraic groups are varieties and groups combined. Varieties are a vast generalization of the fundamental theorem of algebra due to David Hilbert. Chevelley also found the algebraic groups of E8 - the last Lie group not solved by Elie Cartan; it was recently solved by computer around 2001. Armand Borel's book also doesn't get into Hilber's fifth problem about Lie groups.

Coming from another direction, in the eighteen hundreds, mathematicians found invariance theory and abstract algebra through Galois's work. In the nineteen hundreds, Emmy Noether unified both; but quickly, Lie theory in general put even Emmy Noether's great work in (non)commutative algebra in its place in much the same way Newton/Liebniz's calculus put algebra, trigonometry, and geometry in their places, and could solve their problems with comparable ease.

I don't know if it would be correct to consider Lie theory the ultimate mathematics of today; topology probably would stand up and be heard; but, then again they get combined with one another anyways. Overall, this book is a thrill ride and guide to much of the frontier's of modern mathematics.
Was this review helpful? Let us know


Feedback