How Long to Read Maximal Abelian Sets of Roots

How Long Does it Take to Read Maximal Abelian Sets of Roots?

It takes the average reader 3 hours and 46 minutes to read Maximal Abelian Sets of Roots by R. Lawther

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

Description

In this work the author lets be an irreducible root system, with Coxeter group . He considers subsets of which are abelian, meaning that no two roots in the set have sum in . He classifies all maximal abelian sets (i.e., abelian sets properly contained in no other) up to the action of : for each -orbit of maximal abelian sets we provide an explicit representative , identify the (setwise) stabilizer of in , and decompose into -orbits. Abelian sets of roots are closely related to abelian unipotent subgroups of simple algebraic groups, and thus to abelian -subgroups of finite groups of Lie type over fields of characteristic . Parts of the work presented here have been used to confirm the -rank of , and (somewhat unexpectedly) to obtain for the first time the -ranks of the Monster and Baby Monster sporadic groups, together with the double cover of the latter. Root systems of classical type are dealt with quickly here; the vast majority of the present work concerns those of exceptional type. In these root systems the author introduces the notion of a radical set; such a set corresponds to a subgroup of a simple algebraic group lying in the unipotent radical of a certain maximal parabolic subgroup. The classification of radical maximal abelian sets for the larger root systems of exceptional type presents an interesting challenge; it is accomplished by converting the problem to that of classifying certain graphs modulo a particular equivalence relation.

How long is Maximal Abelian Sets of Roots?

Maximal Abelian Sets of Roots by R. Lawther is 219 pages long, and a total of 56,721 words.

This makes it 74% the length of the average book. It also has 69% more words than the average book.

How Long Does it Take to Read Maximal Abelian Sets of Roots Aloud?

The average oral reading speed is 183 words per minute. This means it takes 5 hours and 9 minutes to read Maximal Abelian Sets of Roots aloud.

What Reading Level is Maximal Abelian Sets of Roots?

Maximal Abelian Sets of Roots 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 Maximal Abelian Sets of Roots?

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