## The new encyclopaedia Britannica: in 32 vol. Macropaedia, Accounting - Architecture, Volume 13 |

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Page 301

HOMOLOGY OF

found useful in algebra and arise by taking suitable derived functors. Here one

will be described in which the derived functors are again Tor and Ext functors. If g

is a ...

HOMOLOGY OF

**LIE ALGEBRAS**Many other homology theories have beenfound useful in algebra and arise by taking suitable derived functors. Here one

will be described in which the derived functors are again Tor and Ext functors. If g

is a ...

Page 302

solvable ideal of a

denotes its radical, then G/R has no nonzero radical; such a

semisimple. If a

...

solvable ideal of a

**Lie algebra**is called its radical. If G is a**Lie algebra**and Rdenotes its radical, then G/R has no nonzero radical; such a

**Lie algebra**is calledsemisimple. If a

**Lie algebra**has no nonzero properly smaller ideal, it is Theorems...

Page 512

In the family of Lie groups with a given

others — the so-called universal covering group of the others (also called simply

connected covering group — the one that has no holes). The group of reals is ...

In the family of Lie groups with a given

**Lie algebra**, there is one that covers all theothers — the so-called universal covering group of the others (also called simply

connected covering group — the one that has no holes). The group of reals is ...

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