How Long to Read Lie Superalgebras and Enveloping Algebras

How Long Does it Take to Read Lie Superalgebras and Enveloping Algebras?

It takes the average reader 8 hours and 36 minutes to read Lie Superalgebras and Enveloping Algebras by Ian Malcolm Musson

Assuming a reading speed of 250 words per minute. Learn more

Description

Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. This book develops the theory of Lie superalgebras, their enveloping algebras, and their representations. The book begins with five chapters on the basic properties of Lie superalgebras, including explicit constructions for all the classical simple Lie superalgebras. Borel subalgebras, which are more subtle in this setting, are studied and described. Contragredient Lie superalgebras are introduced, allowing a unified approach to several results, in particular to the existence of an invariant bilinear form on $\mathfrak{g}$. The enveloping algebra of a finite dimensional Lie superalgebra is studied as an extension of the enveloping algebra of the even part of the superalgebra. By developing general methods for studying such extensions, important information on the algebraic structure is obtained, particularly with regard to primitive ideals. Fundamental results, such as the Poincare-Birkhoff-Witt Theorem, are established. Representations of Lie superalgebras provide valuable tools for understanding the algebras themselves, as well as being of primary interest in applications to other fields. Two important classes of representations are the Verma modules and the finite dimensional representations. The fundamental results here include the Jantzen filtration, the Harish-Chandra homomorphism, the Sapovalov determinant, supersymmetric polynomials, and Schur-Weyl duality. Using these tools, the center can be explicitly described in the general linear and orthosymplectic cases. In an effort to make the presentation as self-contained as possible, some background material is included on Lie theory, ring theory, Hopf algebras, and combinatorics.

How long is Lie Superalgebras and Enveloping Algebras?

Lie Superalgebras and Enveloping Algebras by Ian Malcolm Musson is 512 pages long, and a total of 129,024 words.

This makes it 173% the length of the average book. It also has 158% more words than the average book.

How Long Does it Take to Read Lie Superalgebras and Enveloping Algebras Aloud?

The average oral reading speed is 183 words per minute. This means it takes 11 hours and 45 minutes to read Lie Superalgebras and Enveloping Algebras aloud.

What Reading Level is Lie Superalgebras and Enveloping Algebras?

Lie Superalgebras and Enveloping Algebras is suitable for students ages 12 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy Lie Superalgebras and Enveloping Algebras?

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